hey, im having hard time studying the special product of algebra. i cant understand it. can anyone help me?
i have this example, please explain this to me:
(x-y)(x+y)= x2-y2 how it became x2-y2?
(x-y)(x2+xy+y2)=x3-y3 how?
(x+y)(x2-xy+y2)=x3+y3
Special Product in algebra?
2009-07-28 2:21 pm
回答 (10)
2009-07-28 2:35 pm
✔ 最佳答案
Multiply:1. (x-y)(x+y)
= x(x+y) - y(x+y)
= x2+xy-xy-y2 ;[ +xy-xy = 0 ]
= x2-y2
2. (x-y)(x2+xy+y2)
= x(x2+xy+y2) - y(x2+xy+y2)
= x3+x2y+xy2-x2y-xy2-y3 ;[ +x2y+xy2-x2y-xy2 =0 ]
= x3-y3
3. (x+y)(x2-xy+y2)
= x(x2+xy+y2) + y(x2+xy+y2)
= x3-x2y+xy2+x2y-xy2+y3 ;[ -x2y+xy2+x2y-xy2=0 ]
=x3+y3
2009-07-28 2:30 pm
= (x - y)(x + y)
= x(x) + x(y) - y(x) - y(y)
= x² + xy - xy - y²
= x² - y²
= (x - y)(x² + xy + y²)
= x(x²) + x(xy) + x(y²) - y(x²) - y(xy) - y(y²)
= x³ + x²y + xy² - x²y - xy² - y³
= x³ - y³
= (x + y)(x² - xy + y²)
= x(x²) + x(- xy) + x(y²) + y(x²) + y(- xy) + y(y²)
= x³ - x²y + xy² + x²y - xy² + y³
= x³ + y³
= x(x) + x(y) - y(x) - y(y)
= x² + xy - xy - y²
= x² - y²
= (x - y)(x² + xy + y²)
= x(x²) + x(xy) + x(y²) - y(x²) - y(xy) - y(y²)
= x³ + x²y + xy² - x²y - xy² - y³
= x³ - y³
= (x + y)(x² - xy + y²)
= x(x²) + x(- xy) + x(y²) + y(x²) + y(- xy) + y(y²)
= x³ - x²y + xy² + x²y - xy² + y³
= x³ + y³
2009-07-28 3:27 pm
you don't have to do FOIL at all
you need to remember a patter of it
like (x-y)(x+y) = x^2 -y^2
(x+y)(x^2-xy+y^2)= x^3+y^3
(x-y)(x^2+xy+y^2) = x^3 - y^3
you need to remember a patter of it
like (x-y)(x+y) = x^2 -y^2
(x+y)(x^2-xy+y^2)= x^3+y^3
(x-y)(x^2+xy+y^2) = x^3 - y^3
2009-07-28 2:58 pm
You can expand them to know how do they equal to x^2 - y^2, x^3 - y^3 or x^3 + y^3.
(x - y)(x + y)
= x(x) + x(y) - y(x) - y(y)
= x^2 + xy - xy - y^2
= x^2 - y^2
(x - y)(x^2 + xy + y^2)
= x(x^2) + x(xy) + x(y^2) - y(x^2) - y(xy) - y(y^2)
= x^3 + x^2y + xy^2 - x^2y - xy^2 - y^3
= x^3 + x^2y - x^2y + xy^2 - xy^2 - y^3
= x^3 - y^3
(x + y)(x^2 - xy + y^2)
= x(x^2) - x(xy) + x(y^2) + y(x^2) - y(xy) + y(y^2)
= x^3 - x^2y + xy^2 + x^2y - xy^2 + y^3
= x^3 + y^3
(x - y)(x + y)
= x(x) + x(y) - y(x) - y(y)
= x^2 + xy - xy - y^2
= x^2 - y^2
(x - y)(x^2 + xy + y^2)
= x(x^2) + x(xy) + x(y^2) - y(x^2) - y(xy) - y(y^2)
= x^3 + x^2y + xy^2 - x^2y - xy^2 - y^3
= x^3 + x^2y - x^2y + xy^2 - xy^2 - y^3
= x^3 - y^3
(x + y)(x^2 - xy + y^2)
= x(x^2) - x(xy) + x(y^2) + y(x^2) - y(xy) + y(y^2)
= x^3 - x^2y + xy^2 + x^2y - xy^2 + y^3
= x^3 + y^3
2009-07-28 2:44 pm
(x-y)(x+y)
=x^2-xy+xy-y^2 use foil
=x^2-y^2
(x-y)(x^2+xy+y^2) use distributive property
=x^3-xy^2+xy^2-x^2y-xy^2-y^3
=x^3-y^3 answer//
the 3rd one is the same at the 2nd problem..
=x^2-xy+xy-y^2 use foil
=x^2-y^2
(x-y)(x^2+xy+y^2) use distributive property
=x^3-xy^2+xy^2-x^2y-xy^2-y^3
=x^3-y^3 answer//
the 3rd one is the same at the 2nd problem..
2009-07-28 2:27 pm
multiply out each term by foiling, then cancel
1) (x-y)(x+y)= x2-y2 how it became x2-y2
=x^2+xy-xy-y^2... your xy's cancel leaving you with x^2y^2
2) (x-y)(x2+xy+y2)=x3-y3 how?
=x^3+x^2y+xy^2-xy^2+x^2y-y^3 cancel out.. =x^3-y^3
3) (x+y)(x2-xy+y2)=x3+y3
=x^3-x^2y+xy^2+yx^2-xy^2+y^3 cancel out... =x^3+y^3
good luck
1) (x-y)(x+y)= x2-y2 how it became x2-y2
=x^2+xy-xy-y^2... your xy's cancel leaving you with x^2y^2
2) (x-y)(x2+xy+y2)=x3-y3 how?
=x^3+x^2y+xy^2-xy^2+x^2y-y^3 cancel out.. =x^3-y^3
3) (x+y)(x2-xy+y2)=x3+y3
=x^3-x^2y+xy^2+yx^2-xy^2+y^3 cancel out... =x^3+y^3
good luck
2009-07-28 2:26 pm
Foil them and you will see. I'll do the first one
(x-y)(x+y) = x^2 + xy - xy - y^2 = x^2 - y^2
(x-y)(x+y) = x^2 + xy - xy - y^2 = x^2 - y^2
2009-07-28 2:26 pm
multiply the two factors on the left. you'll see that it will end up with the expressions on the right
2016-04-10 8:38 pm
1. First, multiply the first variable of the first equation (2x) with the first variable of the second equation (2x), and you get:4x^2 Second, first variable of the first equation (2x) * second variable of the second equation(-5y),and you get:-10xy Third, second variable of first equation (+5y) * by first variable of second equation (2x), and you get: +10xy Finally, second variable of first equation (+5y) * by second variable of second equation (-5y), and you get: -25y^2 Answer:4x^2 - 25y^2. Answer is D. 2. Same as 1. 3. Never.
2009-07-28 2:27 pm
(x-y)(x+y)=x2+xy-xy-y2
=x2-y2
n u cn slv all of dm jst like dis!!!!!!!!!!!!!!!!!!
=x2-y2
n u cn slv all of dm jst like dis!!!!!!!!!!!!!!!!!!
收錄日期: 2021-05-01 12:39:52
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090728062156AAe9Z1A