Solve 100a^2-(5a+1)^2

$$100 a ^ { 2 } - ( 5 a + 1 ) ^ { 2 }$$

Evaluate

$$\left(5a-1\right)\left(15a+1\right)$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(5a+1\right)^{2}.

$$100a^{2}-\left(25a^{2}+10a+1\right)$$

To find the opposite of 25a^{2}+10a+1, find the opposite of each term.

$$100a^{2}-25a^{2}-10a-1$$

Combine 100a^{2} and -25a^{2} to get 75a^{2}.

$$75a^{2}-10a-1$$

Expand

$$75a^{2}-10a-1$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(5a+1\right)^{2}.

$$100a^{2}-\left(25a^{2}+10a+1\right)$$

To find the opposite of 25a^{2}+10a+1, find the opposite of each term.

$$100a^{2}-25a^{2}-10a-1$$

Combine 100a^{2} and -25a^{2} to get 75a^{2}.

$$75a^{2}-10a-1$$