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Algebra 1 : How to use FOIL in the distributive property

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Example Questions

Example Question #121 : How To Use Foil In The Distributive Property

$(x-1)^{2}$

Multiply. Select the answer that is equivalent to this expression.

Possible Answers:

x^2 + 1

$x^{2} + 2x - 1$

$x^{2} - 2x + 1$

$x^{2} - 1$

2x - 2

Correct answer:

$x^{2} - 2x + 1$

Explanation:

(x-1)^2

Simply write it as a pair and FOIL which stands for the multiplication of the first terms, outer terms, inner terms, and last terms.

= (x-1)(x-1)

= x^2 - x - x + 1

= x^2 - 2x + 1

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Example Question #122 : Distributive Property

(a+b)^2

Multiply. Select the answer that is equivalent to this expression.

Possible Answers:

a^2 + 2ab + b

a^2 + 2ab + b^2

a^2 + ab + b^2

2a + 2b

a^2 + b^2

Correct answer:

a^2 + 2ab + b^2

Explanation:

(a + b)^2

Simply write it as a pair and FOIL which stands for the multiplication of the first terms, outer terms, inner terms, and last terms.

= (a+b)(a+b)

= a^2 + ab+ ab + b^2

= a^2 + 2ab + b^2

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Example Question #123 : Distributive Property

(x+2y)(2x + y)

Multiply. Select the answer that is equivalent to this expression.

Possible Answers:

2x^2 + 4xy + 2y^2

x^2 + 5xy + y^2

2x^2 + 4xy + 3y

y^2 + 4xy + y^2

2x^2 + 5xy + 2y^2

Correct answer:

2x^2 + 5xy + 2y^2

Explanation:

(x + 2y)(2x+y)

For this question use FOIL which stands for the multiplication of the first terms, outer terms, inner terms, and last terms.

= 2x^2 + xy + 4xy + 2y^2

= 2x^2 +5xy + 2y^2

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Example Question #122 : How To Use Foil In The Distributive Property

(x^3 + y)(y^2 + x)

Multiply. Select the answer that is equivalent to this expression.

Possible Answers:

x^3y^2 + x^3 + xy+y^2

x^4 + x^2y + xy + y^3

x^4 + x^3y^2 + xy + y^3

x^3y^2 + x^3 + xy^2 +x^2

x^3 + x^3y^2 + xy + y^3

Correct answer:

x^4 + x^3y^2 + xy + y^3

Explanation:

(x^3 + y)(y^2+x)

Don't be intimidated, just FOIL which stands for the multiplication of the first terms, outer terms, inner terms, and last terms. The answer is rearranged in the order of the powers of x.

= x^3y^2 +x^3x + y^2y +xy

= x^4 + x^3y^2 + xy + y^3

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Example Question #123 : How To Use Foil In The Distributive Property

Expand the following expression:

(9x-6)^2

Possible Answers:

18x^2-18

81x^2-108x+36

81x^2-36

81x^2+36

Correct answer:

81x^2-108x+36

Explanation:

Expand the following expression:

(9x-6)^2

To begin, we need to realize that we cannot simply square both inside terms and call it a day. First, let's rewrite what we are given

(9x-6)^2=(9x-6)(9x-6)

Next, we can use FOIL, which stands for

First

Outer

Inner

Last

$(9x-6)(9x-6)={\color{Red} (9x\cdot9x)}+{\color{Cyan} (9x\cdot-6)}+{\color{DarkBlue} (9x\cdot-6)}+{\color{DarkOrange} (-6 \cdot-6)}$

I've color coded each set, now we just need to simplify and combine like terms to get:

81x^2-108x+36

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Example Question #41 : Quadratic Equations

Use the distributive property (use FOIL method) to solve the following

$\left ( 3+2\right )\left ( 6-4\right )=?$

Possible Answers:

Correct answer:

Explanation:

Remember that FOIL stands for First, Outer, Inner, Last. We will add up the different parts. If we had an expression

$\left ( a+b\right )\left ( c+d\right )$

than we would have

First: $a\times c{}$

Outer: $a \times d$

Inner: $b \times c$

Last: $b \times d$

Foil

For this problem we have

First: $3\times 6=18$

Outer: $3 \times \left (-4 \right )=-12$

Inner: $2 \times 6=12$

Last: $2 \times \left ( -4 \right )=-8$

Adding these together gives

18-12+12-8=10

check: let's add the first two numbers and multiply that by the sum of the last two,

$\left ( 3+2 \right )\left ( 6-4 \right )=5 \times 2=10$

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Example Question #121 : Distributive Property

Foil

(x+b+2)(2x+1) .

Possible Answers:

$2x^{2}+2bx+4x+b$

$2x^{2}+2bx+4x+b+2$

$2x^{2}+2b+5x+2$

$2x^{2}+2bx+5x+b+2$

Correct answer:

$2x^{2}+2bx+5x+b+2$

Explanation:

Multiply the first term of the first factor by the first term of the second factor.

This gives $2x^{2}$ .

Then multiple the first term of the first factor by the second term of the second factor.

This gives .

Then multiply the second term of the first factor by the first term of the second factor to get 2bx .

Multiply the second term of the first factor by the second term of the second factor to get .

Then multply the third term of the first factor by the first term of the second factor to get .

Multiply the third term of the first factor by the second term of the second factor to get .

Finally, add all the terms together (you can do this because all the terms are positive) and combine like terms to get the answer.

$2x^{2}+2bx+5x+b+2$

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Example Question #124 : How To Use Foil In The Distributive Property

Foil

(y+2z)(z+4) .

Possible Answers:

$y^{2}+2z^{2}+8z$

$2z^{2}+8z+4zy+4y$

$2z^{2}+8z+zy+4y$

$z^{2}+4z+2zy+2y$

Correct answer:

$2z^{2}+8z+zy+4y$

Explanation:

Multiply the first term of the first factor by the first term of the second factor to get .

Multiply the first term of the first factor by the second term of the second factor to get .

Multiply the second term of the first factor by the first term of the second factor to get $2z^{2}$ .

Multiply the second term of the first factor by the second term of the second factor to get .

Add these all together and arrange in order of descending exponents to get the answer.

$2z^{2}+8z+zy+4y$

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Example Question #125 : How To Use Foil In The Distributive Property

Foil

x(x+2)(2x-1) .

Possible Answers:

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

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

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

$2x^{3}+5x^{2}-2x$

Correct answer:

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

Explanation:

It's easiest to set aside the x factor for later and just deal with the two factors in parentheses first.

Multiply the first term of the first factor by the first term of the second factor to get $2x^{2}$ .

Multiply the first term of the first factor by the second term of the second factor to get .

Multiply the second term of the first factor by the first term of the second factor to get .

Multiply the second factor of the first term by the second factor of the second term to get .

Then add everything together in order of descending exponentials and combine like terms to get $2x^{2}+3x-2$ .

Then remember to multiply all terms by x to get the final answer!

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

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Example Question #4941 : Algebra 1

Foil

$(c^{2}+2)(c-3)$ .

Possible Answers:

$c^{3}-3c^{2}+2c-6$

$c^{2}-3c+2$

$c^{2}-3c-4$

$3c^{3}-c^{2}+2c-6$

Correct answer:

$c^{3}-3c^{2}+2c-6$

Explanation:

Multiply the first term of the first factor by the first term of the second factor to get $c^{3}$ .

Multiply the first term of the first factor by the second term of the second factor to get $-3c^{2}$ .

Multiply the second term of the first factor by the first term of the second factor to get .

Multiply the second term of the first factor by the second term of the second factor to get .

Finally, add all these terms together in order of decreasing exponentials and paying attention to the negative numbers to get the answer.

$c^{3}-3c^{2}+2c-6$

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Algebra 1 : How to use FOIL in the distributive property

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #121 : How To Use Foil In The Distributive Property

Example Question #122 : Distributive Property

Example Question #123 : Distributive Property

Example Question #122 : How To Use Foil In The Distributive Property

Example Question #123 : How To Use Foil In The Distributive Property

Example Question #41 : Quadratic Equations

Example Question #121 : Distributive Property

Example Question #124 : How To Use Foil In The Distributive Property

Example Question #125 : How To Use Foil In The Distributive Property

Example Question #4941 : Algebra 1

All Algebra 1 Resources

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