Solve (x-1)^2+6(x-1)+9

$$( x - 1 ) ^ { 2 } + 6 ( x - 1 ) + 9$$

Evaluate

$$\left(x+2\right)^{2}$$

Solution Steps

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

$$x^{2}-2x+1+6\left(x-1\right)+9$$

Use the distributive property to multiply 6 by x-1.

$$x^{2}-2x+1+6x-6+9$$

Combine -2x and 6x to get 4x.

$$x^{2}+4x+1-6+9$$

Subtract 6 from 1 to get -5.

$$x^{2}+4x-5+9$$

Add -5 and 9 to get 4.

$$x^{2}+4x+4$$

Expand

$$x^{2}+4x+4$$

Solution Steps

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

$$x^{2}-2x+1+6\left(x-1\right)+9$$

Use the distributive property to multiply 6 by x-1.

$$x^{2}-2x+1+6x-6+9$$

Combine -2x and 6x to get 4x.

$$x^{2}+4x+1-6+9$$

Subtract 6 from 1 to get -5.

$$x^{2}+4x-5+9$$

Add -5 and 9 to get 4.

$$x^{2}+4x+4$$