Solve (u-5)^2-(a+5)^2

$$( u - 5 ) ^ { 2 } - ( a + 5 ) ^ { 2 }$$

Evaluate

$$\left(u-a-10\right)\left(u+a\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(u-5\right)^{2}.

$$u^{2}-10u+25-\left(a+5\right)^{2}$$

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

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

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

$$u^{2}-10u+25-a^{2}-10a-25$$

Subtract 25 from 25 to get 0.

$$u^{2}-10u-a^{2}-10a$$

Expand

$$u^{2}-10u-a^{2}-10a$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(u-5\right)^{2}.

$$u^{2}-10u+25-\left(a+5\right)^{2}$$

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

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

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

$$u^{2}-10u+25-a^{2}-10a-25$$

Subtract 25 from 25 to get 0.

$$u^{2}-10u-a^{2}-10a$$