How to solve Simplify by

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

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Question

$$( x y + y z ) ^ { 2 } - ( x y - y z ) ^ { 2 }$$

Evaluate

$4xzy^{2}$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(xy+yz\right)^{2}$.

$$x^{2}y^{2}+2xyyz+y^{2}z^{2}-\left(xy-yz\right)^{2}$$

Multiply $y$ and $y$ to get $y^{2}$.

$$x^{2}y^{2}+2xy^{2}z+y^{2}z^{2}-\left(xy-yz\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(xy-yz\right)^{2}$.

$$x^{2}y^{2}+2xy^{2}z+y^{2}z^{2}-\left(x^{2}y^{2}-2xyyz+y^{2}z^{2}\right)$$

Multiply $y$ and $y$ to get $y^{2}$.

$$x^{2}y^{2}+2xy^{2}z+y^{2}z^{2}-\left(x^{2}y^{2}-2xy^{2}z+y^{2}z^{2}\right)$$

To find the opposite of $x^{2}y^{2}-2xy^{2}z+y^{2}z^{2}$, find the opposite of each term.

$$x^{2}y^{2}+2xy^{2}z+y^{2}z^{2}-x^{2}y^{2}+2xy^{2}z-y^{2}z^{2}$$

Combine $x^{2}y^{2}$ and $-x^{2}y^{2}$ to get $0$.

$$2xy^{2}z+y^{2}z^{2}+2xy^{2}z-y^{2}z^{2}$$

Combine $2xy^{2}z$ and $2xy^{2}z$ to get $4xy^{2}z$.

$$4xy^{2}z+y^{2}z^{2}-y^{2}z^{2}$$

Combine $y^{2}z^{2}$ and $-y^{2}z^{2}$ to get $0$.

$$4xy^{2}z$$

Show Solution

Expand

$4xzy^{2}$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(xy+yz\right)^{2}$.

$$x^{2}y^{2}+2xyyz+y^{2}z^{2}-\left(xy-yz\right)^{2}$$

Multiply $y$ and $y$ to get $y^{2}$.

$$x^{2}y^{2}+2xy^{2}z+y^{2}z^{2}-\left(xy-yz\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(xy-yz\right)^{2}$.

$$x^{2}y^{2}+2xy^{2}z+y^{2}z^{2}-\left(x^{2}y^{2}-2xyyz+y^{2}z^{2}\right)$$

Multiply $y$ and $y$ to get $y^{2}$.

$$x^{2}y^{2}+2xy^{2}z+y^{2}z^{2}-\left(x^{2}y^{2}-2xy^{2}z+y^{2}z^{2}\right)$$

To find the opposite of $x^{2}y^{2}-2xy^{2}z+y^{2}z^{2}$, find the opposite of each term.

$$x^{2}y^{2}+2xy^{2}z+y^{2}z^{2}-x^{2}y^{2}+2xy^{2}z-y^{2}z^{2}$$

Combine $x^{2}y^{2}$ and $-x^{2}y^{2}$ to get $0$.

$$2xy^{2}z+y^{2}z^{2}+2xy^{2}z-y^{2}z^{2}$$

Combine $2xy^{2}z$ and $2xy^{2}z$ to get $4xy^{2}z$.

$$4xy^{2}z+y^{2}z^{2}-y^{2}z^{2}$$

Combine $y^{2}z^{2}$ and $-y^{2}z^{2}$ to get $0$.

$$4xy^{2}z$$

Show Solution

Basic Math

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Example

Question

Evaluate

Solution Steps

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Solution Steps