Digital SAT · Solve it in Desmos

How to Solve Equivalent Expressions on Desmos (Digital SAT)

Plugging in a number is the fastest, most reliable route on nearly every one of these, and Desmos removes the arithmetic. Do the factoring or expanding by hand only when the numbers are trivial or when the question asks for a specific factored form rather than an equivalent value.

Perfect1600 Content Team·Uses the same Desmos calculator that is built into the Digital SAT

Full method for equivalent expressions

The Desmos steps

1
Type a value for the variable
Enter x = 2 (or any convenient number that keeps denominators nonzero) on its own line in Desmos.
2
Evaluate the original and each choice
Type the original expression and each answer choice; Desmos returns a number for each using your value of x.
3
Keep the match
The choice whose value equals the original is equivalent. For single-variable expressions you can instead graph both and look for one overlapping curve.

Open a real question in the same Desmos calculator you get on Perfect1600, with the setup already typed in:

Worked in Desmos

Easy example

Which expression is equivalent to

6x^{2} + 15x

2x(3x + 5)

3x(2x + 12)

3x(2x + 5)

5x(x + 3)

A: Incorrect. $2x(3x + 5) = 6x^{2} + 10x$ , which has the wrong second term.

B: Incorrect. $3x(2x + 12) = 6x^{2} + 36x$ , which has the wrong second term.

C: Correct. Factoring out $3x$ : $6x^{2} + 15x = 3x(2x + 5)$ .

D: Incorrect. $5x(x + 3) = 5x^{2} + 15x$ , which has the wrong first term.

Explanation

The greatest common factor is $3x$ , so $6x^{2} + 15x = 3x(2x + 5)$ .

Medium example

Which expression is equivalent to

(x + 3)(x + 5)

x^{2} + 8x + 15

x^{2} + 15x + 8

x^{2} + 8x + 8

x^{2} + 15

A: Correct. Using FOIL: $x^{2} + 5x + 3x + 15 = x^{2} + 8x + 15$ .

B: Incorrect. This swaps the sum and product of 3 and 5 in the wrong places.

C: Incorrect. This uses $3 + 5$ for the constant instead of $3 \times 5$ .

D: Incorrect. This omits the middle term $8x$ entirely.

Explanation

Multiply out: $x^{2} + 8x + 15$ .

Hard example

For

x\ne2

, which expression is equivalent to

\dfrac{x^2-4}{x-2}

x-2

x+2

x^2-2

x+4

A: Incorrect. After factoring, the remaining factor is $x+2$ , not $x-2$ .

B: Correct. $\frac{x^2-4}{x-2}=\frac{(x+2)(x-2)}{x-2}=x+2$ for $x\ne2$ .

C: Incorrect. You cannot cancel the $-2$ alone; factor first.

D: Incorrect. $x+4$ does not result from canceling the common factor.

Explanation

Factor and cancel: (x^2-4)/(x-2) = x+2.

Try it with the calculator

Question 1easy

Which expression is equivalent to $(3x^{2} + 2x - 5) + (x^{2} + 4x + 1)$ ?

Question 2easy

Which expression is equivalent to $15x^{2} - 9x^{2}$ ?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

Start the free diagnostic

Desmos questions

Can Desmos solve equivalent expressions questions on the SAT?

Is the Desmos calculator really built into the Digital SAT?

Yes. The Bluebook testing app includes the Desmos graphing calculator on every Math question, so the method here is one you can use on test day, not a workaround.

Should I still learn the algebra?

Yes. Desmos is fastest when you know what to type and what to read. Learn the underlying method on the full guide, then use the calculator to move quickly and to check your work.

Master equivalent expressions, calculator and all

Every Digital SAT question type comes with the method, the Desmos shortcut, and free practice with instant feedback.

See the full method Take the free diagnostic

The Desmos steps

Type a value for the variable

Evaluate the original and each choice

Keep the match

Worked in Desmos

Try it with the calculator

Question 3 is ready when you are

Desmos questions

Can Desmos solve equivalent expressions questions on the SAT?

Is the Desmos calculator really built into the Digital SAT?

Should I still learn the algebra?

Master equivalent expressions, calculator and all