How do you multiply and simplify #\frac { a - 9} { 8} \cdot \frac { 8a + 8} { 8}#?

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Answer 1 · 2017-04-08T01:13:10

See the entire solution process below:

To multiply fractions, you multiply the numerators and you multiply the denominators:

#(a - 9)/8 * (8a + 8)/8 = ((a - 9) * (8a + 8))/(8 * 8) = ((a - 9) * (8a + 8))/64#

Now, we can multiply the two terms in the numerator:

#(8a^2 + 8a - 72a - 72)/64#

We can now combine like terms:

#(8a^2 + (8 - 72)a - 72)/64#

#(8a^2 - 64a - 72)/64#

Now, we can factor an #8# out of each term in the numerator:

#(8(a^2 - 8a - 9))/64#

#(color(red)(cancel(color(black)(8)))(a^2 - 8a - 9))/(color(red)(cancel(color(black)(64)))8)#

#(a^2 - 8a - 9)/8#

Or

#a^2/8 - (8a)/8 - 9/8#

#a^2/8 - a - 9/8#