Using FOIL - High School Math

Card 0 of 12

Question

Solve the equation for .

$\small \frac{1}{x}=\frac{x+1}{6}$

Answer

$\small \small \frac{1}{x}=\frac{x+1}{6}$

Cross multiply.

$\small 6=x(x+1)$

$\small 6=x^2+x$

Set the equation equal to zero.

$\small 0=x^2+x-6$

Factor to find the roots of the polynomial.

and

$\small 0=(x+3)(x-2)$

$\small 0=x+3; x=-3$

$\small 0=x-2; x=2$

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Question

Evaluate $(2x+3)^{2}$

Answer

In order to evaluate $(2x+3)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms.

$\dpi{100} (2x+3)^{2}=(2x+3)(2x+3)$

Multiply terms by way of FOIL method.

Now multiply and simplify.

$=4x^{2}+6x+6x+9$

$\rightarrow 4x^{2}+12x+9$

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Question

Evaluate $(2x+2y)^{2}$

Answer

In order to evaluate $\dpi{100} (2x+2y)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms.

$\dpi{100} \dpi{100} (2x+2y)^{2}=(2x+2y)(2x+2y)$

Multiply terms by way of FOIL method.

Now multiply and simplify.

$=4x^{2}+4xy+4xy+4y^{2}$

$\rightarrow 4x^{2}+8xy+4y^{2}$

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Question

Evaluate $(x-2)^{2}$

Answer

In order to evaluate $\dpi{100} \dpi{100} (x-2)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms. Be sure to pay attention to signs.

$(x-2)^{2}=(x-2)(x-2)$

Multiply terms by way of FOIL method.

Now multiply and simplify, paying attention to signs.

$=x^{2}+(-2x)+(-2x)+4$

$\rightarrow x^{2}-4x+4$

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Question

Evaluate

Answer

In order to evaluate one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms. Be sure to pay attention to signs.

Multiply terms by way of FOIL method.

Now multiply and simplify, paying attention to signs.

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

$\rightarrow 2x^{2}+3xy-2y^{2}$

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Question

Evaluate $(x-y)^{2}$

Answer

In order to evaluate $\dpi{100} \dpi{100} (x-y)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms. Be sure to pay attention to signs.

$(x-y)^{2}=(x-y)(x-y)$

Multiply terms by way of FOIL method.

Now multiply and simplify, paying attention to signs.

$=x^{2}+(-xy)+(-xy)+(y^{2})$

$\rightarrow x^{2}-2xy+y^{2}$

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Question

FOIL .

Answer

Remember FOIL stands for First Outer Inner Last. That means we can take and turn it into .

Simplify to get .

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Question

FOIL .

Answer

is the same thing as .

Remember that FOIL stands for First Outer Inner Last.

For this problem, that would be .

Simplify that to .

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Question

FOIL .

Answer

Remember FOIL stands for First Outer Inner Last.

Combine like terms to get .

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Question

FOIL .

Answer

Remember that FOIL stands for First Outer Inner Last.

For this problem that would give us:

Simplify:

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Question

FOIL .

Answer

Remember that FOIL stands for First Outer Inner Last.

For this problem that would give us:

Simplify.

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Question

Expand .

Answer

To solve our given equation, we need to use FOIL (First, Outer, Inner, Last).

Combine like terms.

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