Solve (2+5)^2-(-3+b)^2

$$( 2 + 5 ) ^ { 2 } - ( - 3 + b ) ^ { 2 }$$

Evaluate

$$\left(10-b\right)\left(b+4\right)$$

Solution Steps

Add 2 and 5 to get 7.

$$7^{2}-\left(-3+b\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

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

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(-3+b\right)^{2}.

$$49-\left(9-6b+b^{2}\right)$$

To find the opposite of 9-6b+b^{2}, find the opposite of each term.

$$49-9+6b-b^{2}$$

Subtract 9 from 49 to get 40.

$$40+6b-b^{2}$$

Expand

$$40+6b-b^{2}$$

Solution Steps

Add 2 and 5 to get 7.

$$7^{2}-\left(-3+b\right)^{2}$$

Calculate 7 to the power of 2 and get 49.

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

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(-3+b\right)^{2}.

$$49-\left(9-6b+b^{2}\right)$$

To find the opposite of 9-6b+b^{2}, find the opposite of each term.

$$49-9+6b-b^{2}$$

Subtract 9 from 49 to get 40.

$$40+6b-b^{2}$$