Solve 64m^2-64m-100m^2+16

$$64 m ^ { 2 } - 64 m - 100 m ^ { 2 } + 16$$

Factor

$$4\left(-m-2\right)\left(9m-2\right)$$

Solution Steps

Factor out 4.

$$4\left(16m^{2}-16m-25m^{2}+4\right)$$

Consider 16m^{2}-16m-25m^{2}+4. Multiply and combine like terms.

$$-9m^{2}-16m+4$$

Consider -9m^{2}-16m+4. Factor the expression by grouping. First, the expression needs to be rewritten as -9m^{2}+am+bm+4. To find a and b, set up a system to be solved.

$$a+b=-16 ab=-9\times 4=-36$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -36.

$$1,-36 2,-18 3,-12 4,-9 6,-6$$

Calculate the sum for each pair.

$$1-36=-35 2-18=-16 3-12=-9 4-9=-5 6-6=0$$

The solution is the pair that gives sum -16.

$$a=2 b=-18$$

Rewrite -9m^{2}-16m+4 as \left(-9m^{2}+2m\right)+\left(-18m+4\right).

$$\left(-9m^{2}+2m\right)+\left(-18m+4\right)$$

Factor out -m in the first and -2 in the second group.

$$-m\left(9m-2\right)-2\left(9m-2\right)$$

Factor out common term 9m-2 by using distributive property.

$$\left(9m-2\right)\left(-m-2\right)$$

Rewrite the complete factored expression.

$$4\left(9m-2\right)\left(-m-2\right)$$

Evaluate

$$16-64m-36m^{2}$$

Solution Steps

Combine 64m^{2} and -100m^{2} to get -36m^{2}.

$$-36m^{2}-64m+16$$