Solve 8h^2-(4h+1)^2+(4h+3)^2=

$$8 h ^ { 2 } - ( 4 h + 1 ) ^ { 2 } + ( 4 h + 3 ) ^ { 2 } =$$

Evaluate

$$8\left(h+1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4h+1\right)^{2}.

$$8h^{2}-\left(16h^{2}+8h+1\right)+\left(4h+3\right)^{2}$$

To find the opposite of 16h^{2}+8h+1, find the opposite of each term.

$$8h^{2}-16h^{2}-8h-1+\left(4h+3\right)^{2}$$

Combine 8h^{2} and -16h^{2} to get -8h^{2}.

$$-8h^{2}-8h-1+\left(4h+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4h+3\right)^{2}.

$$-8h^{2}-8h-1+16h^{2}+24h+9$$

Combine -8h^{2} and 16h^{2} to get 8h^{2}.

$$8h^{2}-8h-1+24h+9$$

Combine -8h and 24h to get 16h.

$$8h^{2}+16h-1+9$$

Add -1 and 9 to get 8.

$$8h^{2}+16h+8$$

Expand

$$8h^{2}+16h+8$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4h+1\right)^{2}.

$$8h^{2}-\left(16h^{2}+8h+1\right)+\left(4h+3\right)^{2}$$

To find the opposite of 16h^{2}+8h+1, find the opposite of each term.

$$8h^{2}-16h^{2}-8h-1+\left(4h+3\right)^{2}$$

Combine 8h^{2} and -16h^{2} to get -8h^{2}.

$$-8h^{2}-8h-1+\left(4h+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4h+3\right)^{2}.

$$-8h^{2}-8h-1+16h^{2}+24h+9$$

Combine -8h^{2} and 16h^{2} to get 8h^{2}.

$$8h^{2}-8h-1+24h+9$$

Combine -8h and 24h to get 16h.

$$8h^{2}+16h-1+9$$

Add -1 and 9 to get 8.

$$8h^{2}+16h+8$$