Solve (2)169(a-b)^2-196(a+b)^2

$$( 2 ) 169 ( a - b ) ^ { 2 } - 196 ( a + b ) ^ { 2 }$$

Evaluate

$$-196\left(a+b\right)^{2}+338\left(a-b\right)^{2}$$

Solution Steps

Multiply 2 and 169 to get 338.

$$338\left(a-b\right)^{2}-196\left(a+b\right)^{2}$$

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

$$338\left(a^{2}-2ab+b^{2}\right)-196\left(a+b\right)^{2}$$

Use the distributive property to multiply 338 by a^{2}-2ab+b^{2}.

$$338a^{2}-676ab+338b^{2}-196\left(a+b\right)^{2}$$

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

$$338a^{2}-676ab+338b^{2}-196\left(a^{2}+2ab+b^{2}\right)$$

Use the distributive property to multiply -196 by a^{2}+2ab+b^{2}.

$$338a^{2}-676ab+338b^{2}-196a^{2}-392ab-196b^{2}$$

Combine 338a^{2} and -196a^{2} to get 142a^{2}.

$$142a^{2}-676ab+338b^{2}-392ab-196b^{2}$$

Combine -676ab and -392ab to get -1068ab.

$$142a^{2}-1068ab+338b^{2}-196b^{2}$$

Combine 338b^{2} and -196b^{2} to get 142b^{2}.

$$142a^{2}-1068ab+142b^{2}$$

Expand

$$142a^{2}-1068ab+142b^{2}$$

Solution Steps

Multiply 2 and 169 to get 338.

$$338\left(a-b\right)^{2}-196\left(a+b\right)^{2}$$

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

$$338\left(a^{2}-2ab+b^{2}\right)-196\left(a+b\right)^{2}$$

Use the distributive property to multiply 338 by a^{2}-2ab+b^{2}.

$$338a^{2}-676ab+338b^{2}-196\left(a+b\right)^{2}$$

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

$$338a^{2}-676ab+338b^{2}-196\left(a^{2}+2ab+b^{2}\right)$$

Use the distributive property to multiply -196 by a^{2}+2ab+b^{2}.

$$338a^{2}-676ab+338b^{2}-196a^{2}-392ab-196b^{2}$$

Combine 338a^{2} and -196a^{2} to get 142a^{2}.

$$142a^{2}-676ab+338b^{2}-392ab-196b^{2}$$

Combine -676ab and -392ab to get -1068ab.

$$142a^{2}-1068ab+338b^{2}-196b^{2}$$

Combine 338b^{2} and -196b^{2} to get 142b^{2}.

$$142a^{2}-1068ab+142b^{2}$$