Solve M=(a+1)^2-(a-1)^2

$$M = ( a + 1 ) ^ { 2 } - ( a - 1 ) ^ { 2 }$$

Solve for M

$$M=4a$$

Solution Steps

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+1\right)^{2}.

$$M=a^{2}+2a+1-\left(a-1\right)^{2}$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-1\right)^{2}.

$$M=a^{2}+2a+1-\left(a^{2}-2a+1\right)$$

To find the opposite of a^{2}-2a+1, find the opposite of each term.

$$M=a^{2}+2a+1-a^{2}+2a-1$$

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

$$M=2a+1+2a-1$$

Combine 2a and 2a to get 4a.

$$M=4a+1-1$$

Subtract 1 from 1 to get 0.

$$M=4a$$

Solve for a

$$a=\frac{M}{4}$$

Steps for Solving Linear Equation

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

$$M=a^{2}+2a+1-\left(a-1\right)^{2}$$

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

$$M=a^{2}+2a+1-\left(a^{2}-2a+1\right)$$

To find the opposite of a^{2}-2a+1, find the opposite of each term.

$$M=a^{2}+2a+1-a^{2}+2a-1$$

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

$$M=2a+1+2a-1$$

Combine 2a and 2a to get 4a.

$$M=4a+1-1$$

Subtract 1 from 1 to get 0.

$$M=4a$$

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

$$4a=M$$

Divide both sides by 4.

$$\frac{4a}{4}=\frac{M}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$a=\frac{M}{4}$$