Solve 2(x-2)^2+(2x-1)(x-4)

$$2 ( x - 2 ) ^ { 2 } + ( 2 x - 1 ) ( x - 4 )$$

Evaluate

$$4x^{2}-17x+12$$

Solution Steps

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

$$2\left(x^{2}-4x+4\right)+\left(2x-1\right)\left(x-4\right)$$

Use the distributive property to multiply 2 by x^{2}-4x+4.

$$2x^{2}-8x+8+\left(2x-1\right)\left(x-4\right)$$

Use the distributive property to multiply 2x-1 by x-4 and combine like terms.

$$2x^{2}-8x+8+2x^{2}-9x+4$$

Combine 2x^{2} and 2x^{2} to get 4x^{2}.

$$4x^{2}-8x+8-9x+4$$

Combine -8x and -9x to get -17x.

$$4x^{2}-17x+8+4$$

Add 8 and 4 to get 12.

$$4x^{2}-17x+12$$

Expand

$$4x^{2}-17x+12$$

Solution Steps

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

$$2\left(x^{2}-4x+4\right)+\left(2x-1\right)\left(x-4\right)$$

Use the distributive property to multiply 2 by x^{2}-4x+4.

$$2x^{2}-8x+8+\left(2x-1\right)\left(x-4\right)$$

Use the distributive property to multiply 2x-1 by x-4 and combine like terms.

$$2x^{2}-8x+8+2x^{2}-9x+4$$

Combine 2x^{2} and 2x^{2} to get 4x^{2}.

$$4x^{2}-8x+8-9x+4$$

Combine -8x and -9x to get -17x.

$$4x^{2}-17x+8+4$$

Add 8 and 4 to get 12.

$$4x^{2}-17x+12$$