How do you multiply and simplify #\frac { x ^ { 2} - 4} { 16} \cdot \frac { 8x ^ { 2} } { x + 2}#?

1 Answer
smendyka
Mar 21, 2017

See the entire solution process below:

Explanation:

#x^2 - 4# is a quadratic of the form:

#(a + b)(a - b) = a^2 - b^2# and therefore can be factored as:

#x^2 - 4 = (x - 2)(x + 2)#

Substituting this into the expression and then cancelling like terms gives:

#((x - 2)(x +2))/16 * (8x^2)/(x + 2) ->#

#((x - 2)color(red)(cancel(color(black)((x +2)))))/(color(blue)(cancel(color(black)(16)))2) * (color(blue)(cancel(color(black)(8)))x^2)/color(red)(cancel(color(black)(x +2))) ->#

#((x - 2)x^2)/2 ->#

#((x * x^2) - (2 * x^2))/2 ->#

#(x^3 - 2x^2)/2#

Or

#x^3/2 - (2x^2)/2 ->#

#x^3/2 - x^2#

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