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How do you find the product #a(-8a^2+2a+4)+3(6a^2-4)#?

Answer 1

See a solution process below:

First, multiply each term inside the parenthesis by the term outside the parenthesis to expand both terms inside the parenthesis:

#color(red)(a)(-8a^2 + 2a + 4) + color(blue)(3)(6a^2 - 4) =>#

#(color(red)(a) xx -8a^2) + (color(red)(a) xx 2a) + (color(red)(a) xx 4) + (color(blue)(3) xx 6a^2) - (color(blue)(3) xx 4) =>#

#-8a^3 + 2a^2 + 4a + 18a^2 - 12#

Next, terms that belong to groups:

#-8a^3 + 2a^2 + 18a^2 + 4a - 12#

Now, blend similar terms together:

#-8a^3 + (2 + 18)a^2 + 4a - 12#

#-8a^3 + 20a^2 + 4a - 12#

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Answer 2

Eli Assouline

To find the product, first distribute each term inside the parentheses, then combine like terms, if any:

a(-8a^2 + 2a + 4) + 3(6a^2 - 4) = -8a^3 + 2a^2 + 4a + 18a^2 - 12

Combine like terms: = -8a^3 + (2a^2 + 18a^2) + 4a - 12 = -8a^3 + 20a^2 + 4a - 12

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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.