Question

What is the missing term in the factorization?

100x^2−36=4(5x+?)(5x−3)

Answer 1

100x^2−36=4(5x+3)(5x−3)

Answer 2

To get the missing terms, we must completely factorize the Left Hand Side of the Equation.

We can do this in two different ways

Method 1

`100x^(2) -36= 4(25x^(2) -9)}`

`\Rightarrow 100x^(2) -36= 4((5x)^(2) -3^2)}`

Using difference of two squares we have

`\Rightarrow 100x^(2) -36= 4(5x+3)(5x-3)}`

By comparing to the given equation, the missing term is

`3`

Method 2

`100x^(2) -36`

`\Rightarrow 100x^(2) -36= (10x)^(2) -6^(2)`

Recall and apply the difference of two squares formula, to obtain,

`100x^(2) -36=(10x+6)(10x-6)`

We can still further factor 2 out of each factor to get,

`100x^(2) -36=2(5x+3) * 2(5x-3)`

`\Rightarrow 100x^(2) -36=2*2(5x+3)(5x-3)`

`\Rightarrow 100x^(2) -36=4(5x+3)(5x-3)`

By comparing to the given equation, the missing term is

`3`