Solve 4(a+b)^2-8(a^2+b^2)

$$4 ( a + b ) ^ { 2 } - 8 ( a ^ { 2 } + b ^ { 2 } )$$

Evaluate

$$-4\left(a-b\right)^{2}$$

Solution Steps

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

$$4\left(a^{2}+2ab+b^{2}\right)-8\left(a^{2}+b^{2}\right)$$

Use the distributive property to multiply 4 by a^{2}+2ab+b^{2}.

$$4a^{2}+8ab+4b^{2}-8\left(a^{2}+b^{2}\right)$$

Use the distributive property to multiply -8 by a^{2}+b^{2}.

$$4a^{2}+8ab+4b^{2}-8a^{2}-8b^{2}$$

Combine 4a^{2} and -8a^{2} to get -4a^{2}.

$$-4a^{2}+8ab+4b^{2}-8b^{2}$$

Combine 4b^{2} and -8b^{2} to get -4b^{2}.

$$-4a^{2}+8ab-4b^{2}$$

Expand

$$-4a^{2}+8ab-4b^{2}$$

Solution Steps

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

$$4\left(a^{2}+2ab+b^{2}\right)-8\left(a^{2}+b^{2}\right)$$

Use the distributive property to multiply 4 by a^{2}+2ab+b^{2}.

$$4a^{2}+8ab+4b^{2}-8\left(a^{2}+b^{2}\right)$$

Use the distributive property to multiply -8 by a^{2}+b^{2}.

$$4a^{2}+8ab+4b^{2}-8a^{2}-8b^{2}$$

Combine 4a^{2} and -8a^{2} to get -4a^{2}.

$$-4a^{2}+8ab+4b^{2}-8b^{2}$$

Combine 4b^{2} and -8b^{2} to get -4b^{2}.

$$-4a^{2}+8ab-4b^{2}$$