Solve 25a^2-16(a-b)^2

$$25 a ^ { 2 } - 16 ( a - b ) ^ { 2 }$$

Evaluate

$$\left(9a-4b\right)\left(a+4b\right)$$

Solution Steps

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

$$25a^{2}-16\left(a^{2}-2ab+b^{2}\right)$$

Use the distributive property to multiply -16 by a^{2}-2ab+b^{2}.

$$25a^{2}-16a^{2}+32ab-16b^{2}$$

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

$$9a^{2}+32ab-16b^{2}$$

Expand

$$9a^{2}+32ab-16b^{2}$$

Solution Steps

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

$$25a^{2}-16\left(a^{2}-2ab+b^{2}\right)$$

Use the distributive property to multiply -16 by a^{2}-2ab+b^{2}.

$$25a^{2}-16a^{2}+32ab-16b^{2}$$

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

$$9a^{2}+32ab-16b^{2}$$