Solve f(x)=2(x-6)^2+100

$$f ( x ) = 2 ( x - 6 ) ^ { 2 } + 100$$

Evaluate

$$2\left(\left(x-6\right)^{2}+50\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$2\left(x^{2}-12x+36\right)+100$$

Use the distributive property to multiply 2 by x^{2}-12x+36.

$$2x^{2}-24x+72+100$$

Add 72 and 100 to get 172.

$$2x^{2}-24x+172$$

Expand

$$2x^{2}-24x+172$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$2\left(x^{2}-12x+36\right)+100$$

Use the distributive property to multiply 2 by x^{2}-12x+36.

$$2x^{2}-24x+72+100$$

Add 72 and 100 to get 172.

$$2x^{2}-24x+172$$