Solve (3p+6)^2-(2p-8)^2

$$( 3 p + 6 ) ^ { 2 } - ( 2 p - 8 ) ^ { 2 }$$

Evaluate

$$\left(5p-2\right)\left(p+14\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3p+6\right)^{2}.

$$9p^{2}+36p+36-\left(2p-8\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2p-8\right)^{2}.

$$9p^{2}+36p+36-\left(4p^{2}-32p+64\right)$$

To find the opposite of 4p^{2}-32p+64, find the opposite of each term.

$$9p^{2}+36p+36-4p^{2}+32p-64$$

Combine 9p^{2} and -4p^{2} to get 5p^{2}.

$$5p^{2}+36p+36+32p-64$$

Combine 36p and 32p to get 68p.

$$5p^{2}+68p+36-64$$

Subtract 64 from 36 to get -28.

$$5p^{2}+68p-28$$

Expand

$$5p^{2}+68p-28$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3p+6\right)^{2}.

$$9p^{2}+36p+36-\left(2p-8\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2p-8\right)^{2}.

$$9p^{2}+36p+36-\left(4p^{2}-32p+64\right)$$

To find the opposite of 4p^{2}-32p+64, find the opposite of each term.

$$9p^{2}+36p+36-4p^{2}+32p-64$$

Combine 9p^{2} and -4p^{2} to get 5p^{2}.

$$5p^{2}+36p+36+32p-64$$

Combine 36p and 32p to get 68p.

$$5p^{2}+68p+36-64$$

Subtract 64 from 36 to get -28.

$$5p^{2}+68p-28$$