(4a-3b)(4a-3b)(4a-3b)?

Question

(4a-3b)^3

how do i even start?

so after the first foil

16a² - 24ab + 9b²

i don't know how i can multipy the third (4a-b) into that trinomal

Answer 1

I'd like to give you the whole answer, but I fear this is a homework question, and you won't learn anything if i just give you the answer. So what I'll do for you is give you a step by step guide on how to solve the answer. You should be able to use the guide for any similar questions. I'm assuming that the question is asking you to expand and evaluate/simplify.

There are three brakets here, it looks a little daunting at first but it really is quite simple.

Ignore one of the brakets so the question is basically
(4a-3b)(4a-3b)

Take your 4a from your frist braket and multiply it to each term (4a and -3b) in your second braket.

ie (4a)(4a-3b) = ((4a)4a - (4a)3b)
= (16a^2 - 12 ab)

Then take the second number (-3b) and do the same thing.

ie (-3b)(4a-3b) = ((-3b)4a - (-3b)3b)
= (-12ab + 9b^2)
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Side Note:
Remember the rule of two negatives = a positive? That's what we just did here:
(-3b) X (-3b) = +12b^2
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Then you add the two results together, also known as collecting like terms (ie, you add/subract all the numbers that have the same endings like a^2 or ab or b^2). Your answer should like like Xa^2 + Yab + Zb^2 (where X, Y and Z are the totals after collecting like terms).

ie (16a^2 - 12 ab) + (-12ab + 9b^2)
= (16a^2 - 12 ab - 12ab + 9b^2)
= (16 a^2 -24 ab + 9b^2)

Now you add the third braket, the one we removed at the beginning, to what we just got from the above work:
ie (4a-3b)(Xa^2 + Yab + Zb^2)
= (4a-3b)(16 a^2 -24ab + 9b^2)

You do the same thing as above. You take your 4a and multiply it to each term in the second bracket. You then take your -3b and multiply to each term in the second bracket. Then you put the two answers together and collect like terms.

ie (4a-3b)(16 a^2 -24ab + 9b^2)
= (4a)(16 a^2 -24ab + 9b^2) + (-3b)(16 a^2 -24ab + 9b^2)

Your answer should look like:

Ka^3 + La^2b + Mab^2 + Nb^3

where K, L, M and N are the totals you get after collecting like terms.

This is exactly what you do when you have questions like this. Just do two brakets at a time and you'll be fine. Pretty soon you'll take on questions like (4a-3b)(4a-3b)(4a-3b)(4a-3b)(4a-3b)!

:p

Hope that helps you out!

Answer 2

6 is the made from 3 and 2 6*a*b = 3*2*a*b 4 is the made from 2 and 2 four*a = 2*2*a hence; 6ab+4a = 3*2*a*b + 2*2*a Take 2*a complication-loose from both the words 6ab+4a = 2*a(3*b + 2) hence (6ab+4a)+(3b+2) = 2a(3b+2) + (3b+2)

Answer 3

Treat it as two separate problems. Start with just the first two binomials. Use FOIL (first, outside, inside, last) to solve:
4a(4a) + -3b(4a) + -3b(4a) + -3b(-3b)
16a^2 -24ab + 9b^2
Then use the same method to multiply this trinomial by the last binomial:
16a^2(4a) + -24ab(4a) + 9b^2(4a) + 16a^2(-3b) + -24ab(-3b) + 9b^2(-3b)
64a^3 -96a^2b + 36ab^2 -48a^2b + 72ab^2 -27b^3
64a^3 -144a^2b +108ab^2 - 27b^3

Answer 4

First do FOIL to (4a-3b)(4a-3b) = 16a^2-24ab+9b^2

Second: (16a^2-24ab+9b^2)(4a-3b)

giving you: 64a^3 -144a^2b +108ab^2 - 27b^3

Answer 5

There are some basic formulas you should remember to make answering questions like this a snap:
(a+b)^2 = a^2 + 2ab + b^2
(a-b)^2 = a^2 - 2ab +b^2
(a-b)(a+b)= a^2 - b^2
(a+b)^3 = a^3 +3a^2b +3ab^2 + b^3
(a-b)^3 = a^3 -3a^2b +3ab^2 - b^3

Jot these down and try to remember them. It wilol save you much time. You might also look up the binomial theorem on the internet.

Answer 6

start w/ the first 2 terms and use FOIL on them
(4a-3b)(4a-3b) to get a new polynomial
keep that new polynomial in parenthesis, then multiply that one by the 3rd (4a - 3b)

Answer 7

Just as (x - y)² ≡x² - 2xy + y²,
(x - y)³ ≡ x³ - 3x²y + 3xy² - y³ (= (x - y)(x² - 2xy + y²))

So (4a - 3b)³ ≡ (4a)³ - 3(4a)²(3b) + 3(4a)(3b)² - (3b)³
= 64a³ - 144a²b + 108ab² - 27b³

Answer 8

4a to the power of 3 - 3b to the power of 3

You can't to it on a keyboard.

Thats it

Answer 9

(4a-3b)(16a^2-24ab+9b^2)
4a(16a^2-24ab+9b^2)=
64a^3-96a^2b+36ab^2
-3b(16a^2-24ab+9b^2)
-48a^2b+72ab^2-27b^3

The answer:
64a^3-144a^2b+108ab^2-27b^3

Answer 10

(4a-3b)^3
=(4a-3b)(4a-3b)(4a-3b)
=(16a^2-12ab-12ab+9b^2)(4a-3b)
=(16a^2-24ab+9b^2)(4a-3b)
=64a^3-96a^2b+36ab^2-48a^2b+72ab^2-27b^3
=64a^3-144a^2b+108ab^2-27b^3