Monomials - SAT Math

Card 0 of 5

Question

Evaluate:

Answer

Distribute the monomial through each term inside the parentheses.

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Question

Multiply:

Answer

Distribute the monomial through the polynomial.

The answer is:

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Question

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

Answer

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:

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Question

Distribute:

Answer

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

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

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Question

Find the product:

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

Answer

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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