Can someone validate this problem for me:
1. Write the product in standard form: (5x-9y) (5x+9y)
---Well, i know that you have to square both the first and last terms seperately, so: First term = 5x, Last term = 9y.
(5x-9y) (5x+9y) = (first term)^2 and (last term) ^2.
= (5x)^2 and (-9y)^2
= 25x^2 + 81y^2
......Is my answer correct, if not please tell me where my mistake was. I would really appreciate it.
2007-09-23 15:06:43 · 5 answers · asked by dana c 1 in Science & Mathematics ➔ Mathematics
no.
If you foil the two binomials together, you get
25x^2 +45xy - 45xy - 9y^2
or 25x^2 - 9y^2
These two binomials are called conjugates - just the same except one is addition and one is subtraction.
They will always end up the first term squared MINUS the second term squared.
2007-09-23 15:11:03 · answer #1 · answered by ccw 4 · 0⤊ 0⤋
You do not square each term separately, but multiply the terms together. The right answer is 25x^2 - 81y^2 (note the minus sign).
(5x + 9x)*(5x - 9x) = 25x^2 -45xy +45xy - 81y^2
the cross product terms (±45xy) cancel out leaving
25x^2 - 81y^2
2007-09-23 15:14:05 · answer #2 · answered by gp4rts 7 · 0⤊ 0⤋
Your answer is correct...
But it's usually written 25x^2 - 81y^2
May I suggest that you forget FOIL and distribute.
FOIL is useless for anything but binomials.
The distributive property of multiplication over addition ALWAYS works. a(b+c)=ab+ac
(5x-9y) (5x+9y)
Distributivity
(5x-9y) (5x+9y) = (5x-9y) (5x) + (5x-9y) (9y)
Using the commutative property of multiplication ab=ba
(5x-9y) (5x) + (5x-9y) (9y) = (5x) (5x-9y) + (9y) (5x-9y)
Distributivity again…
(5x) (5x-9y) + (9y) (5x-9y) = (5x) (5x) + (5x) (-9y) + (9y) (5x) + (9y) (-9y)
Multiplying the stuff out…
(5x) (5x) + (5x) (-9y) + (9y) (5x) + (9y) (-9y) = 25x² - 45xy + 45xy – 81y²
Looking at the two middle terms and again applying the distributive property…
25x² - 45xy + 45xy – 81y² = 25x² + (-45+ 45)xy – 81y²
Now, if you’ll agree that -45+45=0 and that 0xy=0, then you have
(5x-9y) (5x+9y) = 25x² – 81y²
Proving you’re correct.
But there are certain forms of polynomials that become familiar after a while. The difference of squares is one of them. a² - b² = (a+b)(a-b)
2007-09-23 15:11:47 · answer #3 · answered by gugliamo00 7 · 0⤊ 1⤋
stadard form means Ax+By=C
it is wrong here= 25x^-81y^
I will show you an easy way when you have (5x-9y) (5x+9y)
you are multipling postive and postive= postive
negative and negative =postive
negative and postive = negative
2007-09-23 15:15:40 · answer #4 · answered by nazaryan97 2 · 0⤊ 0⤋
9y*-9y= -81y²
2007-09-23 15:10:25 · answer #5 · answered by chasrmck 6 · 0⤊ 0⤋