How to use FOIL with Exponents

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SAT Math › How to use FOIL with Exponents

Questions 1 - 5

1

Simplify:

$\left ( xyz \right )^{3}+x^{2}y+\left ( xy \right )^{0}+\left ( xy^{\frac{1}{2}} \right )^{2}$

$2x^{5}y^{3}z$

$x^{3}y^{3}z^{3}+x^{2}y$

$x^{3}y^{3}z^{3}+2x^{2}y$

$x^{3}y^{3}z^{3}+2x^{2}y+1$

$x^{3}y^{3}z^{3}+x^{2}y+1$

Explanation

$\left ( xyz \right )^{3}+x^{2}y+\left ( xy \right )^{0}+\left ( xy^{\frac{1}{2}} \right )^{2}$

= _x_3_y_3_z_3 + x_2_y + _x_0_y_0 + x_2_y

= _x_3_y_3_z_3 + x_2_y + 1 + x_2_y

= x_3_y_3_z_3 + 2_x_2_y + 1

2

Which of the following is equivalent to 4c(3d)3 – 8c3d + 2(cd)4?

2cd(54d2 – 4c2 + c3 * d3)

2(54d2 – 4c2 + 2c3 * d3)

cd(54c * d3 – 4c3 + c2 * d2)

None of the other answers

Explanation

First calculate each section to yield 4c(27d3) – 8c3d + 2c4d4 = 108cd3 – 8c3d + 2c4d4. Now let's factor out the greatest common factor of the three terms, 2cd, in order to get: 2cd(54d2 – 4c2 + c3d3).

3

Use the FOIL method to simplify the following expression:

Explanation

Use the FOIL method to simplify the following expression:

Step 1: Expand the expression.

Step 2: FOIL

First: $x^3\cdot x^3 = x^6$

Outside: $x^3 \cdot 2x^2 =2x^5$

Inside: $2x^2 \cdot x^3 = 2x^5$

Last: $2x^2 \cdot 2x^2 = 4x^4$

Step 2: Sum the products.

4

If , which of the following could be the value of ?

Explanation

Take the square root of both sides.

$x-3=\pm 5$

$x-3=5\ \text{or}\ x-3=-5$

Add 3 to both sides of each equation.

$x=5+3\ \text{or}\ x=-5+3$

$x=8\ \text{or}\ x=-2$

5

Square the binomial.

$(x^{2}y^{4}+xy^{6})^{2}$

$x^4y^8+2x^3y^{10}+x^2y^{12}$

$x^{4}y^{8}+x^{2}y^{12}$

$x^4y^{16}+2x^2y^{24}+xy^{36}$

$2x^{8}y^{20}$

$x^8y^8+x^2y^{12}$

Explanation

$(x^{2}y^{4}+xy^{6})^{2}$

$(x^{2}y^{4}+xy^{6})(x^{2}y^{4}+xy^{6})$

We will need to FOIL.

First:

Inside: $xy^6*x^2y^4=x^3y^{10}$

Outside: $x^2y^4*xy^6=x^3y^{10}$

Last: $xy^6*xy^6=x^2y^{12}$

Sum all of the terms and simplify.

$x^4y^8+x^3y^{10}+x^3y^{10}+x^2y^{12}$

$x^4y^8+2x^3y^{10}+x^2y^{12}$

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