Solve (y+4)^(2)-(y-2)^(2) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$${ \left(y+4 \right) }^{ 2 } - { \left(y-2 \right) }^{ 2 }$$

Evaluate

$12\left(y+1\right)$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(y+4\right)^{2}$.

$$y^{2}+8y+16-\left(y-2\right)^{2}$$

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

$$y^{2}+8y+16-\left(y^{2}-4y+4\right)$$

To find the opposite of $y^{2}-4y+4$, find the opposite of each term.

$$y^{2}+8y+16-y^{2}+4y-4$$

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

$$8y+16+4y-4$$

Combine $8y$ and $4y$ to get $12y$.

$$12y+16-4$$

Subtract $4$ from $16$ to get $12$.

$$12y+12$$

Expand

$12y+12$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(y+4\right)^{2}$.

$$y^{2}+8y+16-\left(y-2\right)^{2}$$

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

$$y^{2}+8y+16-\left(y^{2}-4y+4\right)$$

To find the opposite of $y^{2}-4y+4$, find the opposite of each term.

$$y^{2}+8y+16-y^{2}+4y-4$$

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

$$8y+16+4y-4$$

Combine $8y$ and $4y$ to get $12y$.

$$12y+16-4$$

Subtract $4$ from $16$ to get $12$.

$$12y+12$$