Solve (3w+5)^2-(w+4)^2

$$( 3 w + 5 ) ^ { 2 } - ( w + 4 ) ^ { 2 }$$

Evaluate

$$\left(2w+1\right)\left(4w+9\right)$$

Solution Steps

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

$$9w^{2}+30w+25-\left(w+4\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(w+4\right)^{2}.

$$9w^{2}+30w+25-\left(w^{2}+8w+16\right)$$

To find the opposite of w^{2}+8w+16, find the opposite of each term.

$$9w^{2}+30w+25-w^{2}-8w-16$$

Combine 9w^{2} and -w^{2} to get 8w^{2}.

$$8w^{2}+30w+25-8w-16$$

Combine 30w and -8w to get 22w.

$$8w^{2}+22w+25-16$$

Subtract 16 from 25 to get 9.

$$8w^{2}+22w+9$$

Expand

$$8w^{2}+22w+9$$

Solution Steps

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

$$9w^{2}+30w+25-\left(w+4\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(w+4\right)^{2}.

$$9w^{2}+30w+25-\left(w^{2}+8w+16\right)$$

To find the opposite of w^{2}+8w+16, find the opposite of each term.

$$9w^{2}+30w+25-w^{2}-8w-16$$

Combine 9w^{2} and -w^{2} to get 8w^{2}.

$$8w^{2}+30w+25-8w-16$$

Combine 30w and -8w to get 22w.

$$8w^{2}+22w+25-16$$

Subtract 16 from 25 to get 9.

$$8w^{2}+22w+9$$