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

Answer 1

See the entire solution process below:

To multiply these two terms together you multiply each of the terms within the left parenthesis by each of the terms in the right parenthesis:

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

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

#a^2 - 3a - 7a + 21#

Now, combine like terms:

#a^2 + (-3 - 7)a + 21#

#a^2 - 10a + 21#

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Answer 2

Savannah Anderson

To multiply ( (a - 7)(a - 3) ), you can use the distributive property or the FOIL method:

Using the distributive property: ( (a - 7)(a - 3) = a(a - 3) - 7(a - 3) ) ( = a^2 - 3a - 7a + 21 ) ( = a^2 - 10a + 21 )

Using the FOIL method: ( (a - 7)(a - 3) = a^2 - 3a - 7a + 21 ) ( = a^2 - 10a + 21 )

So, ( (a - 7)(a - 3) = a^2 - 10a + 21 ).

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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.