Solve 10x^2-(7x+1)^2

$$10 x ^ { 2 } - ( 7 x + 1 ) ^ { 2 }$$

Evaluate

$$-39x^{2}-14x-1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(7x+1\right)^{2}.

$$10x^{2}-\left(49x^{2}+14x+1\right)$$

To find the opposite of 49x^{2}+14x+1, find the opposite of each term.

$$10x^{2}-49x^{2}-14x-1$$

Combine 10x^{2} and -49x^{2} to get -39x^{2}.

$$-39x^{2}-14x-1$$

Expand

$$-39x^{2}-14x-1$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(7x+1\right)^{2}.

$$10x^{2}-\left(49x^{2}+14x+1\right)$$

To find the opposite of 49x^{2}+14x+1, find the opposite of each term.

$$10x^{2}-49x^{2}-14x-1$$

Combine 10x^{2} and -49x^{2} to get -39x^{2}.

$$-39x^{2}-14x-1$$