2 answers
(click or scroll down)
Factor each expression
a^2(b-c)-16b^2(b-c)
Help show me how
(b-c) appears in both terms and can be factored out, giving you
(b-c)(a^2-16b^2)
Now note that the second term can also be factored since it is the difference of two perfect squares.
(a^2-16b^2) = (a+4b)(a-4b)
Make that substitution and you will have factored the original expression into three terms.
Julia
answered16 years ago
Explain Bot
answered11 months ago
To factor the expression a^2(b-c)-16b^2(b-c), we can use the distributive property to first factor out the common factor (b-c) from both terms:
a^2(b-c) - 16b^2(b-c)
This gives us:
(b-c)(a^2 - 16b^2)
Next, we can look at the remaining part of the expression, which is (a^2 - 16b^2). This is a difference of squares, since a^2 can be written as (a)^2 and 16b^2 can be written as (4b)^2.
Therefore, (a^2 - 16b^2) can be factored into:
(a^2 - 16b^2) = (a + 4b)(a - 4b)
Now, substituting this factored form back into the original expression, we get:
(b - c)(a + 4b)(a - 4b)
So the fully factored form of the expression a^2(b-c)-16b^2(b-c) is (b - c)(a + 4b)(a - 4b).