Why not use 0, 1 or 2 as the number?

At 0 every term with an x in it vanishes, so wrong choices that differ only in those terms look right. At 1 every power of x equals 1, and at 2 the expressions 2x and x^2 give the same value. A number such as 3 is far less likely to hide a wrong choice.

What if two choices give the same number?

Try a second number on those two. One number can match by accident: x^2 and 3x both give 9 at x = 3, but they differ at every other number except 0. A second number separates choices that a first number could not.

Does a match at one number prove two expressions are equivalent?

No. A match fails to rule a choice out, while a mismatch rules it out for good. On a question with one equivalent choice, the choice that survives two numbers is the answer. If you want proof, expand or factor and compare.

Can I type the expression and the choices into the calculator instead?

Yes. Type the question's expression as f(x) = ... and a choice as g(x) = ... If the choice is equivalent, its graph lies exactly on top of the first, and f(3) and g(3) print the same number. Use ^ for powers and put brackets around anything on the bottom of a fraction, such as (x + 1)/(x - 2).

Which number should I choose if the expression has a fraction?

One that makes no denominator zero, in the question or in any choice. Read the denominators first. For x^2 - 9 over x - 3, avoid 3 and -3, then use something like 4 or 5.

What if the question asks for a constant in a rewritten form?

When the choices are values of a, b or c in a form such as a(x - h)^2 + k, expand the form and match coefficients. Testing a number would mean solving for the constants anyway.

Find the equivalent expression by putting a number in

Put the same number, not 0, 1 or 2, into the question's expression and into each choice. The choice that gives the same number is the equivalent one. If two match, try a second number.

1.Pick a number for $x$ that is not 0, 1 or 2 and does not make a denominator zero. 3 usually works. At 0 every term with an $x$ in it disappears, and at 1 and 2 different expressions can give the same value.
2.Put it into the expression in the question and note the result. Put the same number into each choice. Keep the choices that give the same result and cross out the rest.
3.If two choices match, try a second number on those two. Do not stop at the first match.
4.Or let the calculator do the putting in: type the expression as $f(x)$ and a choice as $g(x)$ . If the graph of $g$ lies exactly on top of $f$ , the choice is equivalent, and $f(3)$ and $g(3)$ print the same number.

Try it on a question

Work it below before you open the working. The steps say what to do, and you can do each one yourself.

Which expression is equivalent to $(5x - 2)(2x + 3)$ ?

Choice A: $10x^2 - 6$
Choice B: $10x^2 + 11x - 6$
Choice C: $10x^2 + 19x - 6$
Choice D: $10x^2 + 11x + 6$

1
Type the expression from the question as $f(x)$ , exactly as it is printed. Its curve is drawn: a parabola, because the product has an $x^2$ in it.
Type: f(x) = (5x - 2)(2x + 3)
2
Type the choice you want to test as $g(x)$ . If it is equivalent, its curve is drawn exactly over $f$ 's and you cannot see $f$ any more. A choice that is not equivalent leaves a second curve beside the first.
Type: g(x) = 10x^2 + 11x - 6
3
Type f(3). A number that is not 0, 1 or 2 gives a result that tells the choices apart. It prints 117.
Type: f(3)
4
Type g(3). It prints 117 as well. Same curve and same number: this choice is equivalent.
Type: g(3)
5
Find the answer in the rows. The number a row prints is beside it.

Open in the full calculator

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The full working, and why each wrong choice is there

Pick $x = 3$ , which is not 0, 1 or 2. The expression gives $(15 - 2)(6 + 3) = 13 \cdot 9 = 117$ . Now try each choice at 3: the first gives $90 - 6 = 84$ , the second gives $90 + 33 - 6 = 117$ , the third gives $90 + 57 - 6 = 141$ and the fourth gives $90 + 33 + 6 = 129$ . Only the second matches.

By hand, the expansion is $10x^2 + 15x - 4x - 6 = 10x^2 + 11x - 6$ , which agrees. In the calculator: type the expression as $f(x)$ and the choice as $g(x)$ . The two graphs lie on top of each other, and $f(3)$ and $g(3)$ both print 117.

Choice A: $10x^2 - 6$
This multiplies the first terms and the last terms only. The two $x$ -terms, $5x \cdot 3$ and $-2 \cdot 2x$ , are missing. At $x = 3$ it gives 84, and the expression gives 117.
Choice B: $10x^2 + 11x - 6$ the answer
The middle term is $15x - 4x = 11x$ and the last term is $(-2)(3) = -6$ . At $x = 3$ it gives 117, the same as the expression.
Choice C: $10x^2 + 19x - 6$
The $-2 \cdot 2x$ term was added instead of subtracted, giving $15x + 4x$ . At $x = 3$ it gives 141, not 117.
Choice D: $10x^2 + 11x + 6$
The last term should be $(-2)(3) = -6$ , not $+6$ . At $x = 3$ it gives 129, not 117.

Use it when

The question asks which choice is equivalent to a given expression, and everything is written in terms of $x$ .
The algebra is long: several brackets, a fraction, or powers. A number check is quicker than a full rewrite and harder to slip on.
You have rewritten the expression yourself and want a ten-second proof before you choose.
The choices look alike and differ only in a sign or a coefficient. One number separates them.

Do not use it when

A choice can agree with the expression at one number by accident, so a single match is not proof. Whenever two choices give the same number, try a second number before you commit.
The question asks for a constant, such as $a$ , $b$ or $c$ in a rewritten form. Expanding the form and matching coefficients is faster than testing choices.
The number you pick makes a denominator zero, as 3 does in $\frac{x^2 - 9}{x - 3}$ . The result is an error, not a number, so choose another.

Five questions on this move

Untimed, and nothing is saved. A wrong first answer gets one more try before the working is shown.

Question 1 of 5

Which expression is equivalent to $(2x - 5)^2 - 4x^2$ ?

Five is a start

In your account there is a focused set of ten on Equivalent expressions from the question bank, with the same one more try. And after each practice test, the drills your plan sets for the skills you missed name the moves for them.

Practise Equivalent expressions in your account

How this page was checked

Every maths answer, by our own calculator
The answer to each of the 6 questions on this page is worked out again by our calculator engine in an automated test, which fails when a key disagrees with the engine.
In the calculator the test uses
Claude (an AI assistant) typed this page's calculator steps into the College Board version of the Desmos calculator on 14 October 2026 and read the same answers. The walk-through was typed in exactly as printed: the second graph lies exactly on the first, and f(3) and g(3) both print 117.
The whole page, by a person
Not yet. Every question and every step of its walk-through was worked through in a browser by Claude, an AI assistant, on 14 October 2026. The page was published on 14 October 2026 before a person had read it. If something here is wrong, tell us and it is put right.

The questions were drafted with AI and are original: none is a College Board question, and none comes from the question bank behind our practice tests.

Where this comes from

“Put a number in, or graph the choices” is one card from the Preptics lesson Equivalent expressions: the four wrong rewrites, which sits under the Digital SAT skill Equivalent expressions. The lesson has the other cards around it, and its questions come back for review on a schedule. The lessons are part of the Digital SAT track.

Common questions

Why not use 0, 1 or 2 as the number?: At 0 every term with an x in it vanishes, so wrong choices that differ only in those terms look right. At 1 every power of x equals 1, and at 2 the expressions 2x and x^2 give the same value. A number such as 3 is far less likely to hide a wrong choice.
What if two choices give the same number?: Try a second number on those two. One number can match by accident: x^2 and 3x both give 9 at x = 3, but they differ at every other number except 0. A second number separates choices that a first number could not.
Does a match at one number prove two expressions are equivalent?: No. A match fails to rule a choice out, while a mismatch rules it out for good. On a question with one equivalent choice, the choice that survives two numbers is the answer. If you want proof, expand or factor and compare.
Can I type the expression and the choices into the calculator instead?: Yes. Type the question's expression as f(x) = ... and a choice as g(x) = ... If the choice is equivalent, its graph lies exactly on top of the first, and f(3) and g(3) print the same number. Use ^ for powers and put brackets around anything on the bottom of a fraction, such as (x + 1)/(x - 2).
Which number should I choose if the expression has a fraction?: One that makes no denominator zero, in the question or in any choice. Read the denominators first. For x^2 - 9 over x - 3, avoid 3 and -3, then use something like 4 or 5.
What if the question asks for a constant in a rewritten form?: When the choices are values of a, b or c in a form such as a(x - h)^2 + k, expand the form and match coefficients. Testing a number would mean solving for the constants anyway.

Keep going

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