Solve 32x^2+28x+56x+49

$$32 x ^ { 2 } + 28 x + 56 x + 49$$

Factor

$$\left(4x+7\right)\left(8x+7\right)$$

Solution Steps

Multiply and combine like terms.

$$32x^{2}+84x+49$$

Factor the expression by grouping. First, the expression needs to be rewritten as 32x^{2}+ax+bx+49. To find a and b, set up a system to be solved.

$$a+b=84 ab=32\times 49=1568$$

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 1568.

$$1,1568 2,784 4,392 7,224 8,196 14,112 16,98 28,56 32,49$$

Calculate the sum for each pair.

$$1+1568=1569 2+784=786 4+392=396 7+224=231 8+196=204 14+112=126 16+98=114 28+56=84 32+49=81$$

The solution is the pair that gives sum 84.

$$a=28 b=56$$

Rewrite 32x^{2}+84x+49 as \left(32x^{2}+28x\right)+\left(56x+49\right).

$$\left(32x^{2}+28x\right)+\left(56x+49\right)$$

Factor out 4x in the first and 7 in the second group.

$$4x\left(8x+7\right)+7\left(8x+7\right)$$

Factor out common term 8x+7 by using distributive property.

$$\left(8x+7\right)\left(4x+7\right)$$

Evaluate

$$\left(4x+7\right)\left(8x+7\right)$$

Solution Steps

Combine 28x and 56x to get 84x.

$$32x^{2}+84x+49$$