PLEASE HELP I UNDERSTAND HOW THEY GOT THE FIRST PART OF THE ANSWER BUT THE 12XY IM LOST ON
2007-08-16 07:03:28 · 10 answers · asked by pouncey03 1 in Science & Mathematics ➔ Mathematics
Rewrite the equation and use FOIL (first, outside, inside, last):
(3x-2y)(3x-2y)
= 9x^2 - 6xy - 6xy + 4y^2
= 9x^2 - 12xy + 4y^2
Note: the ordering of the terms doesn't matter, as long as you keep the signs with the terms.
2007-08-16 07:11:32 · answer #1 · answered by Larry C 3 · 0⤊ 0⤋
(3x - 2y)^2 is the same as multiplying the polynomial twice: (3x - 2y)*(3x - 2y). When multiplying polynomials, the basic concept is that you have to multiply each factor on one side by all the factors on the other side, and then add them all up.
For example, say you wanted to multiply (10+2)*(3+4). You would first multiply 10 by all the factors on the left, then the 2 by all the factors on the left, and add everything together.
(10+2)(3+4) = 10*3 + 10*4 + 2*3 + 2*4
= 30+40+6+8
= 84
(Now just a back track, that's the same as 12*7 = 84!)
So the same goes with this.
(3x-2y)(3x-2y) = 3x*3x + 3x(-2y) + (-2y)*3x + (-2y)(-2y)
= 9x^2 - 6xy - 6xy + 4y^2
= 9x^2 + 4y^2 - 12xy
2007-08-16 07:13:42 · answer #2 · answered by Anonymous · 1⤊ 0⤋
Well, in (3x-2y)(3x-2y), the 3x is multiplied by the -2y, and the -2y is multiplied by 3x. This results in 2 * -6xy = -12xy.
2007-08-16 07:12:51 · answer #3 · answered by John V 6 · 0⤊ 0⤋
Just multiply all the terms together
(3X-2Y)^2 = (3X)^2 + (2Y)^2 +(3X)(-2Y) + (3X)(-2Y)
(3X-2Y)^2 = 9X^2 + 4Y^2 - 12xy
2007-08-16 07:13:14 · answer #4 · answered by Captain Mephisto 7 · 0⤊ 0⤋
its a square of a binomial:
where if you are given (a-b)^2 it is equal to (a^2-2ab+b^2).. so
(3x-2y)^2 = ((3x)^2 - ((2)(3x)(2y)) + (-2y)^2)
=9x^2-12xy+4y^2
2007-08-16 07:20:45 · answer #5 · answered by acinom 1 · 0⤊ 0⤋
It can also be written as (3X-2Y)(3X-2Y). Then you have to multiply everything. So you get:
3X*3X=9XX (9X^2)
3X*2Y=6XY
2Y*3X=6XY
-2Y*-2Y=4YY (4Y^2)
Then you combine like terms.
9X^2-12XY+4Y^2
2007-08-16 07:15:44 · answer #6 · answered by Anonymous · 0⤊ 0⤋
The above answers explain it pretty well, just try to memorize as a general rule...
(x+y)^2 = x^2 + 2xy + y^2
(x-y)^2 = x^2 - 2xy + y^2
2007-08-16 07:14:06 · answer #7 · answered by Michael W 3 · 0⤊ 0⤋
(3x-2y)Ë2 = (3x-2y)(3x-2y)
3x(3x-2y) - 2y(3x-2y)
9xË2 - 6xy - 6xy + 4yË2
9xËx -12xy + 4yË2
gluck
2007-08-16 07:11:50 · answer #8 · answered by mcauslan 2 · 0⤊ 0⤋
IT'S FOIL TIME!
(3X-2Y)^2 = (3X-2Y)(3X-2Y)
O + I = -6XY + -6XY = -12XY.
2007-08-16 07:10:52 · answer #9 · answered by Anonymous · 0⤊ 0⤋
I have a head ache now!!!!
2007-08-16 07:11:39 · answer #10 · answered by SWT 6 · 0⤊ 0⤋