Solve 49x^2-left(3x+5right)^2

$$49 { x }^{ 2 } - { \left(3x+5 \right) }^{ 2 }$$

Evaluate

$$40x^{2}-30x-25$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+5\right)^{2}.

$$49x^{2}-\left(9x^{2}+30x+25\right)$$

To find the opposite of 9x^{2}+30x+25, find the opposite of each term.

$$49x^{2}-9x^{2}-30x-25$$

Combine 49x^{2} and -9x^{2} to get 40x^{2}.

$$40x^{2}-30x-25$$

Expand

$$40x^{2}-30x-25$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+5\right)^{2}.

$$49x^{2}-\left(9x^{2}+30x+25\right)$$

To find the opposite of 9x^{2}+30x+25, find the opposite of each term.

$$49x^{2}-9x^{2}-30x-25$$

Combine 49x^{2} and -9x^{2} to get 40x^{2}.

$$40x^{2}-30x-25$$