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How do you multiply #(3a-7b)^2#?

Answer 1

See the entire multiplication process below:

This problem can be rewritten as:

#(color(red)(3a) - color(red)(7b))(color(blue)(3a) - color(blue)(7b))#

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(3a) - color(red)(7b))(color(blue)(3a) - color(blue)(7b))# becomes:

#(color(red)(3a) xx color(blue)(3a)) - (color(red)(3a) xx color(blue)(7b)) - (color(red)(7b) xx color(blue)(3a)) + (color(red)(7b) xx color(blue)(7b))#

#9a^2 - 21ab - 21ab + 49b^2#

We can now combine like terms:

#9a^2 + (-21 - 21)ab + 49b^2#

#9a^2 - 42ab + 49b^2#

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Answer 2

Abigail Allen

To multiply ((3a - 7b)^2), you apply the formula for squaring a binomial, which is ((a - b)^2 = a^2 - 2ab + b^2). So, in this case, you get ( (3a)^2 - 2(3a)(7b) + (-7b)^2), which simplifies to (9a^2 - 42ab + 49b^2).

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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.