Solve F=(a+4)^2-(a-4)^2

$$F = ( a + 4 ) ^ { 2 } - ( a - 4 ) ^ { 2 }$$

Solve for F

$$F=16a$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+4\right)^{2}.

$$F=a^{2}+8a+16-\left(a-4\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-4\right)^{2}.

$$F=a^{2}+8a+16-\left(a^{2}-8a+16\right)$$

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

$$F=a^{2}+8a+16-a^{2}+8a-16$$

Combine a^{2} and -a^{2} to get 0.

$$F=8a+16+8a-16$$

Combine 8a and 8a to get 16a.

$$F=16a+16-16$$

Subtract 16 from 16 to get 0.

$$F=16a$$

Solve for a

$$a=\frac{F}{16}$$

Steps for Solving Linear Equation

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

$$F=a^{2}+8a+16-\left(a-4\right)^{2}$$

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

$$F=a^{2}+8a+16-\left(a^{2}-8a+16\right)$$

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

$$F=a^{2}+8a+16-a^{2}+8a-16$$

Combine a^{2} and -a^{2} to get 0.

$$F=8a+16+8a-16$$

Combine 8a and 8a to get 16a.

$$F=16a+16-16$$

Subtract 16 from 16 to get 0.

$$F=16a$$

Swap sides so that all variable terms are on the left hand side.

$$16a=F$$

Divide both sides by 16.

$$\frac{16a}{16}=\frac{F}{16}$$

Dividing by 16 undoes the multiplication by 16.

$$a=\frac{F}{16}$$