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

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

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Answer 1 · 2017-04-24T19:56:00

$\frac{x - 4}{2 x}$ $(x-4)/(2x)$

Explanation:

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

$(x - 4) (4 x^{3} + 10 x^{2})$ $(x-4)(4x^3+10x^2)$

Remember we multiply every term with each other.
So,

$(x \cdot 4 x^{3}) + (x \cdot 10 x^{2}) + (- 4 \cdot 4 x^{3}) + (- 4 \cdot 10 x^{2})$ $(x*4x^3)+(x*10x^2)+(-4*4x^3)+(-4*10x^2)$

$4 x^{4} + 10 x^{3} - 16 x^{3} - 40 x^{2}$ $4x^4+10x^3-16x^3-40x^2$

[Simplify common variables]

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

$4 x^{4} - 6 x^{3} - 40 x^{2}$ $4x^4-6x^3-40x^2$

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

$(4 x^{2} + 10 x) (2 x^{2})$ $(4x^2+10x)(2x^2)$

$(4 x^{2} \cdot 2 x^{2}) + (10 x \cdot 2 x^{2})$ $(4x^2*2x^2)+(10x*2x^2)$

$8 x^{4} + 20 x^{3}$ $8x^4+20x^3$

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

and our denominator
$8 x^{4} + 20 x^{3}$ $8x^4+20x^3$

$\frac{4 x^{4} - 6 x^{3} - 40 x^{2}}{8 x^{4} + 20 x^{3}}$ $(4x^4-6x^3-40x^2)/(8x^4+20x^3)$

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

$\frac{2 x^{2} (2 x^{2} - 3 x - 20)}{4 x^{3} (2 x + 5)}$ $(2x^2(2x^2-3x-20))/(4x^3(2x+5))$

Divide our common factor

$\frac{(2 x^{2} - 3 x - 20)}{2 x (2 x + 5)}$ $((2x^2-3x-20))/(2x(2x+5))$

$\frac{2 x^{2} - 3 x - 20}{2 x (2 x + 5)}$ $(2x^2-3x-20)/(2x(2x+5)$

Factor the numerator using whatever method your prefer.
[Look here if you are confused on how I factored the numerator.](https://www.mathsisfun.com/algebra/factoring-quadratics.html)
Your result should be

$\frac{(x - 4) (2 x + 5)}{2 x (2 x + 5)}$ $((x-4)(2x+5))/(2x(2x+5)$

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

$(x-4)/(2x)$

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

1 Answer

Explanation:

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How do you multiply \frac { x - 4} { 4x ^ { 2} + 10x } \cdot \frac { 4x ^ { 3} + 10x ^ { 2} } { 2x ^ { 2} }x−44x2+10x⋅4x3+10x22x2\frac { x - 4} { 4x ^ { 2} + 10x } \cdot \frac { 4x ^ { 3} + 10x ^ { 2} } { 2x ^ { 2} }?

1 Answer

Explanation:

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