Solve 2*(a-b)^2+2a*(a-20)^2

$$2 \cdot ( a - b ) ^ { 2 } + 2 a \cdot ( a - 20 ) ^ { 2 }$$

Evaluate

$$2\left(a\left(a-20\right)^{2}+\left(a-b\right)^{2}\right)$$

Solution Steps

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

$$2\left(a^{2}-2ab+b^{2}\right)+2a\left(a-20\right)^{2}$$

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

$$2a^{2}-4ab+2b^{2}+2a\left(a-20\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-20\right)^{2}.

$$2a^{2}-4ab+2b^{2}+2a\left(a^{2}-40a+400\right)$$

Use the distributive property to multiply 2a by a^{2}-40a+400.

$$2a^{2}-4ab+2b^{2}+2a^{3}-80a^{2}+800a$$

Combine 2a^{2} and -80a^{2} to get -78a^{2}.

$$-78a^{2}-4ab+2b^{2}+2a^{3}+800a$$

Expand

$$2a^{3}-78a^{2}-4ab+800a+2b^{2}$$

Solution Steps

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

$$2\left(a^{2}-2ab+b^{2}\right)+2a\left(a-20\right)^{2}$$

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

$$2a^{2}-4ab+2b^{2}+2a\left(a-20\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-20\right)^{2}.

$$2a^{2}-4ab+2b^{2}+2a\left(a^{2}-40a+400\right)$$

Use the distributive property to multiply 2a by a^{2}-40a+400.

$$2a^{2}-4ab+2b^{2}+2a^{3}-80a^{2}+800a$$

Combine 2a^{2} and -80a^{2} to get -78a^{2}.

$$-78a^{2}-4ab+2b^{2}+2a^{3}+800a$$