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SAT Math : Monomials

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Example Questions

Example Question #1 : Monomials

Multiply: (1-x^2)(9x)

Possible Answers:

9x^3-1

-1-9x^3

-x^2+9x+1

9x-9x^3

9x^3-9x

Correct answer:

9x-9x^3

Explanation:

Distribute the monomial through the polynomial.

(1-x^2)(9x)= 9x-9x^3

The answer is: 9x-9x^3

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Example Question #1 : Variables

Evaluate: 3x(x^2+3x-1)

Possible Answers:

3x^3-9x^2+3x

3x^3+x^2-x

4x^3-6x-3x

3x^3+9x^2-3x

4x^3+6x-3x

Correct answer:

3x^3+9x^2-3x

Explanation:

Distribute the monomial through each term inside the parentheses.

3x(x^2+3x-1)= 3x(x^2)+(3x)(3x)+(3x)(-1)

= 3x^3+9x^2-3x

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Example Question #2 : Variables

Multiply the monomials: $6x \times 4x^2$

Possible Answers:

$\textup{They are not like terms, so they can't be multiplied.}$

24x^3

48x^3

72x

24x^2

Correct answer:

24x^3

Explanation:

In order to multiply this, we can simply multiply the coefficients together and the variables together. Anytime we multiply a variable of the same base, we can add the exponents.

$6x \times 4x^2 = (6\cdot 4) (x^1\cdot x^2)$

Simplify the right side.

$(6\cdot 4) (x^1\cdot x^2) = 24(x^{1+2})= 24x^3$

The answer is: 24x^3

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Example Question #1 : Variables

Distribute: 4ab(3a-5b+1)

Possible Answers:

-8ab-1

12a^2b-20ab^2

12a^2b+20ab^2+4ab

12a^2b-20ab^2+4ab

-8ab+1

Correct answer:

12a^2b-20ab^2+4ab

Explanation:

Distribute the monomial to each part of the polynomial, paying careful attention to signs:

4ab(3a-5b+1)

$4ab\cdot3a+4ab\cdot(-5b)+4ab\cdot1$

12a^2b-20ab^2+4ab

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Example Question #2 : Monomials

Find the product:

$\left ( \frac{5x^3y^5}{y^6z^4} \right )\left ( \frac{2xy^{-1}}{3zx^2} \right )$

Possible Answers:

$\frac{10x^2}{3y^2z^5}$

$\frac{10x^3}{z^4}$

$\frac{x}{y^4}$

$\frac{5y^6}{2xz^4}$

x^2z^4

Correct answer:

$\frac{10x^2}{3y^2z^5}$

Explanation:

Find the product:

$\left ( \frac{5x^3y^5}{y^6z^4} \right )\left ( \frac{2xy^{-1}}{3zx^2} \right )$

Step 1: Multiply the numerators and denominators using the properties of exponents. (When multiplying exponents, add them.)

$\frac{5x^3y^5\cdot 2xy^{-1}}{y^6z^4\cdot 3zx^2}$

$\frac{10x^4y^4}{3y^6z^5x^2}$

Step 2: Simplify the expression.

$\frac{10x^2}{3y^2z^5}$

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SAT Math : Monomials

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Monomials

Example Question #1 : Variables

Example Question #2 : Variables

Example Question #1 : Variables

Example Question #2 : Monomials

All SAT Math Resources

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