Solve {c}{9(a+b)^2-25(a}{-b)^2}

$$\left. \begin{array} { c } { 9 ( a + b ) ^ { 2 } - 25 ( a } \\ { - b ) ^ { 2 } } \end{array} \right.$$

Evaluate

$$4\left(4a-b\right)\left(4b-a\right)$$

Solution Steps

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

$$9\left(a^{2}+2ab+b^{2}\right)-25\left(a-b\right)^{2}$$

Use the distributive property to multiply 9 by a^{2}+2ab+b^{2}.

$$9a^{2}+18ab+9b^{2}-25\left(a-b\right)^{2}$$

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

$$9a^{2}+18ab+9b^{2}-25\left(a^{2}-2ab+b^{2}\right)$$

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

$$9a^{2}+18ab+9b^{2}-25a^{2}+50ab-25b^{2}$$

Combine 9a^{2} and -25a^{2} to get -16a^{2}.

$$-16a^{2}+18ab+9b^{2}+50ab-25b^{2}$$

Combine 18ab and 50ab to get 68ab.

$$-16a^{2}+68ab+9b^{2}-25b^{2}$$

Combine 9b^{2} and -25b^{2} to get -16b^{2}.

$$-16a^{2}+68ab-16b^{2}$$

Expand

$$-16a^{2}+68ab-16b^{2}$$

Solution Steps

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

$$9\left(a^{2}+2ab+b^{2}\right)-25\left(a-b\right)^{2}$$

Use the distributive property to multiply 9 by a^{2}+2ab+b^{2}.

$$9a^{2}+18ab+9b^{2}-25\left(a-b\right)^{2}$$

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

$$9a^{2}+18ab+9b^{2}-25\left(a^{2}-2ab+b^{2}\right)$$

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

$$9a^{2}+18ab+9b^{2}-25a^{2}+50ab-25b^{2}$$

Combine 9a^{2} and -25a^{2} to get -16a^{2}.

$$-16a^{2}+18ab+9b^{2}+50ab-25b^{2}$$

Combine 18ab and 50ab to get 68ab.

$$-16a^{2}+68ab+9b^{2}-25b^{2}$$

Combine 9b^{2} and -25b^{2} to get -16b^{2}.

$$-16a^{2}+68ab-16b^{2}$$