Solve (1-2x)^2+(x+2)^2-5(x^2-2)

$$( 1 - 2 x ) ^ { 2 } + ( x + 2 ) ^ { 2 } - 5 ( x ^ { 2 } - 2 )$$

Evaluate

$$15$$

Solution Steps

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

$$1-4x+4x^{2}+\left(x+2\right)^{2}-5\left(x^{2}-2\right)$$

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

$$1-4x+4x^{2}+x^{2}+4x+4-5\left(x^{2}-2\right)$$

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$1-4x+5x^{2}+4x+4-5\left(x^{2}-2\right)$$

Combine -4x and 4x to get 0.

$$1+5x^{2}+4-5\left(x^{2}-2\right)$$

Add 1 and 4 to get 5.

$$5+5x^{2}-5\left(x^{2}-2\right)$$

Use the distributive property to multiply -5 by x^{2}-2.

$$5+5x^{2}-5x^{2}+10$$

Combine 5x^{2} and -5x^{2} to get 0.

$$5+10$$

Add 5 and 10 to get 15.

$$15$$

Factor

$$3\times 5$$