(3a - 2b)(3a - 2b) Polynomials x Binomials?

Question

I see they went 3a * 3a = 9a^2, but where does the 12ab come from? Can someone pls spell this out for me? =)


answer is 9a^2 - 12ab + 4b^2

Answer 1

think FOIL

(a+b)(c-d)

First (multiply the first term in each binomial, a*c)
Inside (multiply the 2 inside terms, b*c)
Outside (multiply the 2 outside terms, a*-d)
Last (multiply the last term in each binomial, b*-d)

then add them all up:
ac+bc-ad-bd

Answer 2

First: take the first term (3a) from the first set and multiply it by the first coefficient (3a) from the second setL 3a(3a) = 9a^2

Second: take the first term (3a) from the first set and multiply it with the second term (-2b) from the second set: (3a)(-2b) = -6ab

Third: take the second term (-2b) from the first set and multiply it by the first term (3a) from the second set: (-2b)(3a) = -6ab

Fourth: take the second term (-2b) from the first set and multiply it by the second term (-2b) from the second set:
(-2b)(-2b)= 4b^2

*Now rewrite this expression without parenthesis and combine "like" terms:

= 9a^2 - 6ab - 6ab + 4b^2
= 9a^2 - 12ab + 4b^2

Answer 3

(3a - 2b)(3a - 2b)okay, so first you multiply 3a by 3a. which is 9a^2 next, you multiply 3a by -2b, which is negative 6ab, then, you multiply -2b by 3a, which is -6ab. After that, multiply -2b by -2b, and you get 4b^2. Then you simplify it, and then you would get 9a^2-12ab+4b^2 You get the 12ab by adding the two -6ab's together!! Good luck with algebra!!

Answer 4

First 3a x (-2b) = -6ab; 3a from 1st bracket and -2b from the second

then (-2b) x 3a = -6ab; -2b from 1st bracket and 3a from the second

add the two, -12ab

Answer 5

(3a-2b)(3a-2b) = 9a^2-6ab-6ab+4b^2 = 9a^2-12ab+4b^2.

Answer 6

(3a-2b)(3a-2b) =
9a^2 - 6ab-6ab + 4b^2 =
9a^2 - 12ab + 4b^2

Answer 7

(3a - 2b)(3a - 2b) is the factored form of 9a^2 - 12ab + 4b^2.

What it means is that you multiply everything out.
(3a - 2b)(3a - 2b)
....-> (3a x 3a) + (3a x -2b) + (-2b x 3a) + (-2b x -2b)
.................-> 9a^2 + -6ab + -6ab + 4b^2
...........................-> 9a^2 + -12ab + 4b^2
.......................................-> 9a^2 - 12ab + 4b^2

12ab comes from the distribution rule of multiplication, where:
3a - 2b must be multiplied by 3a - 2b, and 3a must be taken to each term of 3a - 2b. This leads to 3a x 3a and 3a x -2b.

Visually (where each must be multiplied to):
..........|-----|-----|
(3a - 2b)(3a - 2b)
...|-----------|-----|

Answer 8

a million. (x + 2)(x + 8) = x² + 10x + sixteen 2. (x - 5)(x - eleven) = x² - 16x - fifty 5 <-- must be +fifty 5 3. (x + 3)(x - 8) = x² - 5x - 24 4. (3x - 5)(3x + 2) = 9x² - 9x - 10 5. (x + 5)(x + 7) = x² + 12x + 35 6. (2x - a million)(x + 8) = x² + 15 - 8 <-- 15x somewhat of 15 and 2x^2 somewhat of x^2 7. (2x - 3)(2x + a million) = 4x² - 4x - 3 8. (3x + 2)(2x + 6) = 6x² + 16x + 12 <-- 22x somewhat of 16x

Answer 9

(3a - 2b)(3a - 2b)

= (3a)(3a) - (3a)(2b) - (2b)(3a) + (-2b)(-2b)

= (3a)^2 - 6ab - 6ab + (-2b)^2

= 9a^2 - 12ab + 4b^2

Answer 10

(3a-2b)(3a-2b)
9a^2-6ab-6ab+4b^2
9a^2-12ab+4b^2

I hope this helps!