Distributive Property

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SAT Math › Distributive Property

Questions 1 - 10

1

Expand the expression $(x^{4}+2x^{3})(4x+9)$ .

$4x^{5}+17x^{4}+18x^{3}$

$4x^{3}+11x^{2}+13x$

$5x^{4}+13x^{3}+8x^{2}$

$6x^{4}+5x^{3}+11x$

$9x^{4}+8x^{3}+11x^{2}$

Explanation

Use the FOIL method (first, outer, inner, last) to multiply expressions and combine like terms:

$(x^{4}+2x^{3})(4x+9)$

$=(x^4 \cdot4x) + (x^4 \cdot 9) + (2x^3 \cdot 4x) + (2x^3\cdot 9)$

$=4x^{5}+9x^{4}+8x^{4}+18x^{3}$

$=4x^{5}+17x^{4}+18x^{3}$

2

Expand the expression $(x^{4}+2x^{3})(4x+9)$ .

$4x^{5}+17x^{4}+18x^{3}$

$4x^{3}+11x^{2}+13x$

$5x^{4}+13x^{3}+8x^{2}$

$6x^{4}+5x^{3}+11x$

$9x^{4}+8x^{3}+11x^{2}$

Explanation

Use the FOIL method (first, outer, inner, last) to multiply expressions and combine like terms:

$(x^{4}+2x^{3})(4x+9)$

$=(x^4 \cdot4x) + (x^4 \cdot 9) + (2x^3 \cdot 4x) + (2x^3\cdot 9)$

$=4x^{5}+9x^{4}+8x^{4}+18x^{3}$

$=4x^{5}+17x^{4}+18x^{3}$

3

Expand the expression $(x^{4}+2x^{3})(4x+9)$ .

$4x^{5}+17x^{4}+18x^{3}$

$4x^{3}+11x^{2}+13x$

$5x^{4}+13x^{3}+8x^{2}$

$6x^{4}+5x^{3}+11x$

$9x^{4}+8x^{3}+11x^{2}$

Explanation

Use the FOIL method (first, outer, inner, last) to multiply expressions and combine like terms:

$(x^{4}+2x^{3})(4x+9)$

$=(x^4 \cdot4x) + (x^4 \cdot 9) + (2x^3 \cdot 4x) + (2x^3\cdot 9)$

$=4x^{5}+9x^{4}+8x^{4}+18x^{3}$

$=4x^{5}+17x^{4}+18x^{3}$

4

Use FOIL to multiply the expressions:

$x^{2}-6x+8$

$x^{2}-6x-8$

$2x^{2}-6x+8$

$x^{2}-8x+8$

Explanation

The term FOIL stands for First, Outside, Inside, Last. It refers to the order in which you distribute between the two expressions, which allows each monomial to multiplied by each monomial in the neighboring expression. For this problem that would look like this:

$x^{2}-2x-4x+8$

$x^{2}-6x+8$

5

Use FOIL to multiply the expressions:

$x^{2}-6x+8$

$x^{2}-6x-8$

$2x^{2}-6x+8$

$x^{2}-8x+8$

Explanation

The term FOIL stands for First, Outside, Inside, Last. It refers to the order in which you distribute between the two expressions, which allows each monomial to multiplied by each monomial in the neighboring expression. For this problem that would look like this:

$x^{2}-2x-4x+8$

$x^{2}-6x+8$

6

Use FOIL to multiply the expressions:

$x^{2}-6x+8$

$x^{2}-6x-8$

$2x^{2}-6x+8$

$x^{2}-8x+8$

Explanation

The term FOIL stands for First, Outside, Inside, Last. It refers to the order in which you distribute between the two expressions, which allows each monomial to multiplied by each monomial in the neighboring expression. For this problem that would look like this:

$x^{2}-2x-4x+8$

$x^{2}-6x+8$

7

Given the equation above, what is the value of ?

Explanation

Use FOIL to expand the left side of the equation.

From this equation, we can solve for , , and .

$18x^2=ax^2\rightarrow a=18$

$24x=dx\rightarrow d=24$

Plug these values into to solve.

8

If , what is the value of ?

$\pm\frac{4\sqrt{2}}{5}$

$\pm2\sqrt{2}$

$\pm\frac{4}{5}$

$\pm5\sqrt{3}$

$\pm7$

Explanation

Use the FOIL method to distribute terms and simplify the equation:

$25x^{2}-16=16$

$25x^{2}=32$

$x^{2}=\frac{32}{25}$

$x=\pm \sqrt{\frac{32}{25}}$

$x=\pm \frac{\sqrt{16}\sqrt{2}}{5}$

$x=\pm \frac{4\sqrt{2}}{5}$

9

If , what is the value of ?

$\pm\frac{4\sqrt{2}}{5}$

$\pm2\sqrt{2}$

$\pm\frac{4}{5}$

$\pm5\sqrt{3}$

$\pm7$

Explanation

Use the FOIL method to distribute terms and simplify the equation:

$25x^{2}-16=16$

$25x^{2}=32$

$x^{2}=\frac{32}{25}$

$x=\pm \sqrt{\frac{32}{25}}$

$x=\pm \frac{\sqrt{16}\sqrt{2}}{5}$

$x=\pm \frac{4\sqrt{2}}{5}$

10

Given the equation above, what is the value of ?

Explanation

Use FOIL to expand the left side of the equation.

From this equation, we can solve for , , and .

$18x^2=ax^2\rightarrow a=18$

$24x=dx\rightarrow d=24$

Plug these values into to solve.

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