How do you multiply \frac { x - 4} { 4x ^ { 2} + 10x } \cdot \frac { 4x ^ { 3} + 10x ^ { 2} } { 2x ^ { 2} }?

1 Answer
Apr 24, 2017

(x-4)/(2x)

Explanation:

When multiplying fractions we simply multiply across.
Let's start with the numerators.

(x-4)(4x^3+10x^2)

Remember we multiply every term with each other.
So,

(x*4x^3)+(x*10x^2)+(-4*4x^3)+(-4*10x^2)

4x^4+10x^3-16x^3-40x^2

[Simplify common variables]

4x^4color(red)(+10x^3-16x^3)-40x^2

4x^4-6x^3-40x^2

color(blue)"Now we do the same for the denominators"

(4x^2+10x)(2x^2)

(4x^2*2x^2)+(10x*2x^2)

8x^4+20x^3

So now we have...
our numerator
4x^4-6x^3-40x^2

and our denominator
8x^4+20x^3

(4x^4-6x^3-40x^2)/(8x^4+20x^3)

Now look for common factors to simplify our fraction.
I found 2x^2 in the numerator and 4x^3 in the denominator

(2x^2(2x^2-3x-20))/(4x^3(2x+5))

Divide our common factor

((2x^2-3x-20))/(2x(2x+5))

(2x^2-3x-20)/(2x(2x+5)

Factor the numerator using whatever method your prefer.
Look here if you are confused on how I factored the numerator.
Your result should be

((x-4)(2x+5))/(2x(2x+5)

((x-4)cancel((2x+5)))/(2xcancel((2x+5))

(x-4)/(2x)