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PSAT Math : How to use FOIL with Exponents

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Example Questions

Example Question #1161 : Algebra

If $\displaystyle (x-3)^2=25$ , which of the following could be the value of $\displaystyle x$ ?

Possible Answers:

$\displaystyle 2$

$\displaystyle -2$

$\displaystyle 3$

$\displaystyle -5$

$\displaystyle 5$

Correct answer:

$\displaystyle -2$

Explanation:

$\displaystyle (x-3)^2=25$

Take the square root of both sides.

$x-3=\pm 5$ $\displaystyle x-3=\pm 5$

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

Add 3 to both sides of each equation.

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

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

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Example Question #1162 : Algebra

Simplify:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

= x³y³z³ + x²y + x⁰y⁰ + x²y

= x³y³z³ + x²y + 1 + x²y

= x³y³z³ + 2x²y + 1

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Example Question #5 : Exponents And The Distributive Property

$\displaystyle (6x^4+2x^2)(3x^4+6x^2)$

Possible Answers:

42x^8 $\displaystyle 42x^8$

$\displaystyle 18x^8+42x^6+12x^4$

$\displaystyle 18x^8+36x^6+12x^4$

$\displaystyle 18x^8+12x^4$

$18x^{16}+42x^8+12x^4$ $\displaystyle 18x^{16}+42x^8+12x^4$

Correct answer:

$\displaystyle 18x^8+42x^6+12x^4$

Explanation:

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

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

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

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

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

Add all the terms:

$\displaystyle 18x^8+36x^6+6x^6+12x^4$

$\displaystyle 18x^8+42x^6+12x^4$

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Example Question #5 : How To Use Foil With Exponents

Square the binomial.

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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

We will need to FOIL.

First: $\displaystyle x^2y^4*x^2y^4=x^4y^8$

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

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

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

Sum all of the terms and simplify.

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

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

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Example Question #1164 : Algebra

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

Possible Answers:

2cd(54d² – 4c²+ c³* d³)

2(54d²– 4c²+ 2c³* d³)

None of the other answers

cd(54c * d³– 4c³+ c²* d²)

Correct answer:

2cd(54d² – 4c²+ c³* d³)

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).

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PSAT Math : How to use FOIL with Exponents

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1161 : Algebra

Example Question #1162 : Algebra

Example Question #5 : Exponents And The Distributive Property

Example Question #5 : How To Use Foil With Exponents

Example Question #1164 : Algebra

All PSAT Math Resources

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