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

Answer 1

Eva Adamson

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#

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

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

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Answer 2

Kennedy Adams

To multiply and simplify the given expression, follow these steps:

Multiply the numerators: ( (a - 9) \cdot (8a + 8) ).
Multiply the denominators: ( 8 \cdot 8 ).
Simplify the result if possible.

The simplified expression is: (\frac {a^2 - a - 72} {8}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.