How to use FOIL with Exponents - PSAT Math

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Question

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

Answer

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.

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

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

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Question

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

Answer

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).

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Question

Simplify:

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

Answer

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

= _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

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Question

Square the binomial.

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

Answer

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

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

We will need to FOIL.

First:

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

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

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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Question

Answer

Use the FOIL method to find the product. Remember to add the exponents when multiplying.

First: $6x^4\cdot3x^4 = 18x^8$

Outside: $6x^4\cdot6x^2=36x^6$

Inside: $2x^2\cdot 3x^4=6x^6$

Last: $2x^2\cdot6x^2=12x^4$

Add all the terms:

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