Solve (9a-2)^2-25(b+1)^2

$$( 9 a - 2 ) ^ { 2 } - 25 ( b + 1 ) ^ { 2 }$$

Evaluate

$$\left(9a-5b-7\right)\left(9a+5b+3\right)$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(9a-2\right)^{2}.

$$81a^{2}-36a+4-25\left(b+1\right)^{2}$$

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

$$81a^{2}-36a+4-25\left(b^{2}+2b+1\right)$$

Use the distributive property to multiply -25 by b^{2}+2b+1.

$$81a^{2}-36a+4-25b^{2}-50b-25$$

Subtract 25 from 4 to get -21.

$$81a^{2}-36a-21-25b^{2}-50b$$

Expand

$$81a^{2}-36a-25b^{2}-50b-21$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(9a-2\right)^{2}.

$$81a^{2}-36a+4-25\left(b+1\right)^{2}$$

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

$$81a^{2}-36a+4-25\left(b^{2}+2b+1\right)$$

Use the distributive property to multiply -25 by b^{2}+2b+1.

$$81a^{2}-36a+4-25b^{2}-50b-25$$

Subtract 25 from 4 to get -21.

$$81a^{2}-36a-21-25b^{2}-50b$$