Solve x^2+8x-4x+4

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

Factor

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

Solution Steps

Multiply and combine like terms.

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

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+4. To find a and b, set up a system to be solved.

$$a+b=4 ab=1\times 4=4$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 4.

$$1,4 2,2$$

Calculate the sum for each pair.

$$1+4=5 2+2=4$$

The solution is the pair that gives sum 4.

$$a=2 b=2$$

Rewrite x^{2}+4x+4 as \left(x^{2}+2x\right)+\left(2x+4\right).

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

Factor out x in the first and 2 in the second group.

$$x\left(x+2\right)+2\left(x+2\right)$$

Factor out common term x+2 by using distributive property.

$$\left(x+2\right)\left(x+2\right)$$

Rewrite as a binomial square.

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

Evaluate

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

Solution Steps

Combine 8x and -4x to get 4x.

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