Solve left(x-4right)^2-6(x-4)+9

$${ \left(x-4 \right) }^{ 2 } -6(x-4)+9$$

Evaluate

$$\left(x-7\right)^{2}$$

Solution Steps

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

$$x^{2}-8x+16-6\left(x-4\right)+9$$

Use the distributive property to multiply -6 by x-4.

$$x^{2}-8x+16-6x+24+9$$

Combine -8x and -6x to get -14x.

$$x^{2}-14x+16+24+9$$

Add 16 and 24 to get 40.

$$x^{2}-14x+40+9$$

Add 40 and 9 to get 49.

$$x^{2}-14x+49$$

Expand

$$x^{2}-14x+49$$

Solution Steps

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

$$x^{2}-8x+16-6\left(x-4\right)+9$$

Use the distributive property to multiply -6 by x-4.

$$x^{2}-8x+16-6x+24+9$$

Combine -8x and -6x to get -14x.

$$x^{2}-14x+16+24+9$$

Add 16 and 24 to get 40.

$$x^{2}-14x+40+9$$

Add 40 and 9 to get 49.

$$x^{2}-14x+49$$