How to use FOIL in the distributive property

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SAT Math › How to use FOIL in the 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

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:

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

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

3

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.

4

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:

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

$25x^{2}=32$

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

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

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

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

5

Expand and simplify the expression.

$8x^{2}-200$

$8x^{2}-80x-200$

$8x^{2}-40x+200$

$8x^{2}-200x$

Explanation

We can solve by FOIL, then distribute the $\small 4$ . Since all terms are being multiplied, you will get the same answer if you distribute the $\small 4$ before using FOIL.

First:

Inside:

Outside:

Last:

Sum all of the terms and simplify. Do not forget the $\small 4$ in front of the quadratic!

Finally, distribute the $\small 4$ .

6

Expand and simplify:

$(2\sqrt{7}+\sqrt{8})^{2}=$

$36+8\sqrt{14}$

$4\sqrt{15}$

$4+\sqrt{15}$

$8+7\sqrt{15}$

$7+8\sqrt{56}$

Explanation

Use the FOIL method in the distributive property to simplify the expression:

$(2\sqrt{7}+\sqrt{8})^{2}$

First simplify the radicals,

$=(2\sqrt{7}+\sqrt{4}\sqrt{2})^{2}$

$=(2\sqrt{7}+2\sqrt{2})^{2}$

$=(2\sqrt{7}+2\sqrt{2})(2\sqrt{7}+2\sqrt{2})$

$=(4)(7)+(4\sqrt{2}\sqrt{7}+4\sqrt{2}\sqrt{7})+(4)(2)$

$=28+4\sqrt{14}+4\sqrt{14}+8$

$=36+8\sqrt{14}$

7

Expand the expression:

$\dpi{100} \small (x^{3}-4x)(6 + 12x^{2})$

$\dpi{100} \small 12x^{5}-42x^{3}-24x$

$\dpi{100} \small 42x^{3}+12x^{5}-24x$

$\dpi{100} \small 6x^{3} + 12x^{5}-24x-48x^{3}$

$\dpi{100} \small 6x^{3} + 12x^{2}-24x-48$

$\dpi{100} \small 22x^{2}$

Explanation

When using FOIL, multiply the first, outside, inside, then last expressions; then combine like terms.

$\dpi{100} \small (x^{3}-4x)(6 + 12x^{2})$

$\dpi{100} \small 6x^{3}+12x^{5}-24x-48x^{3}$

$\dpi{100} \small -42x^{3}+12x^{5}-24x$

$\dpi{100} \small 12x^{5}-42x^{3}-24x$

8

Use FOIL to multiply the expressions:

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

$x^{4}+13x^{2}+36$

$x^{4}-13x^{2}+36$

$2x^{4}+13x^{2}+36$

$x^{4}+36x^{2}+13$

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:

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

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

$x^{4}+9x^{2}+4x^{2}+36$

$x^{4}+13x^{2}+36$

9

Use FOIL to multiply the expressions:

$5x^{2}-9x-18$

$x^{2}-9x-18$

$5x^{2}-12x-18$

$3x^{2}-15x-9$

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:

$5x^{2}-15x+6x-18$

$5x^{2}-9x-18$

10

Use FOIL to multiply the expressions:

$3x^{2}+34x-24$

$3x^{2}-34x-24$

$2x^{2}+34x-14$

$2x^{2}+34x+24$

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:

$3x^{2}-2x+36x-24$

$3x^{2}+34x-24$

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