all formula for polynomial
Akankshyasahu5968:
thank you hardy
Ya quadrilateral chapter ka ha question
pahala Mera solution do
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Answers
Answered by
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(x + y)2 = x2 + 2xy + y2
(x - y)2 = x2 - 2xy + y2
(-x + y)2 = (y - x)2 = y2 - 2xy + x2
(-x - y)2 = (-(x + y))2 = (x + y)2 = x2 + 2xy + y2
(x + y)3 = x3 + 3x2y + 3xy2 + y3
(x - y)3 = x3 - 3x2y + 3xy2 - y3
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2xz + 2yz
(x - y - z)2 = x2 + y2 + z2 - 2xy - 2xz + 2yz
Factor Rules
x2 - y2 = (x - y)(x + y)
x2 + y2 = (x + y)2 - 2xy
or
x2 + y2 = (x - y)2 + 2xy
x3 - y3 = (x - y)(x2 + xy + y2)
x3 + y3 = (x + y)(x2 - xy + y2)
If n is a natural number
xn - yn = (x - y)(xn-1 + xn-2y +...+ yn-2x + yn-1)
If n is even (n = 2k)
xn + yn = (x + y)(xn-1 - xn-2y +...+ yn-2x - yn-1)
If n is odd (n = 2k + 1)
xn + yn = (x + y)(xn-1 - xn-2y +...- yn-2x + yn-1)
More Algebraic Formulas
2(a2 + b2) = (a + b)2 + (a - b)2
(a + b)2 - (a - b)2 = 4ab
(a - b)2 = (a + b)2 - 4ab
a4 + b4 = (a + b)(a - b)[(a + b)2 - 2ab]
I hope this will help you.☺️
(x - y)2 = x2 - 2xy + y2
(-x + y)2 = (y - x)2 = y2 - 2xy + x2
(-x - y)2 = (-(x + y))2 = (x + y)2 = x2 + 2xy + y2
(x + y)3 = x3 + 3x2y + 3xy2 + y3
(x - y)3 = x3 - 3x2y + 3xy2 - y3
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2xz + 2yz
(x - y - z)2 = x2 + y2 + z2 - 2xy - 2xz + 2yz
Factor Rules
x2 - y2 = (x - y)(x + y)
x2 + y2 = (x + y)2 - 2xy
or
x2 + y2 = (x - y)2 + 2xy
x3 - y3 = (x - y)(x2 + xy + y2)
x3 + y3 = (x + y)(x2 - xy + y2)
If n is a natural number
xn - yn = (x - y)(xn-1 + xn-2y +...+ yn-2x + yn-1)
If n is even (n = 2k)
xn + yn = (x + y)(xn-1 - xn-2y +...+ yn-2x - yn-1)
If n is odd (n = 2k + 1)
xn + yn = (x + y)(xn-1 - xn-2y +...- yn-2x + yn-1)
More Algebraic Formulas
2(a2 + b2) = (a + b)2 + (a - b)2
(a + b)2 - (a - b)2 = 4ab
(a - b)2 = (a + b)2 - 4ab
a4 + b4 = (a + b)(a - b)[(a + b)2 - 2ab]
I hope this will help you.☺️
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welcome dear
Answered by
3
✨✨hey mate here is your ans.-✨✨
Polynomial Identities
polynomial identities(short multiplication formulas):
(x + y)2 = x2 + 2xy + y2
(x - y)2 = x2 - 2xy + y2
polynomial identities(short multiplication formulas):
(x + y)2 = x2 + 2xy + y2
(x - y)2 = x2 - 2xy + y2
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2xz + 2yz
(x - y - z)2 = x2 + y2 + z2 - 2xy - 2xz + 2yz
Factor Rules
x2 - y2 = (x - y)(x + y)
x2 + y2 = (x + y)2 - 2xy
or
x2 + y2 = (x - y)2 + 2xy
If n is a natural number
xn - yn = (x - y)(xn-1 + xn-2y +...+ yn-2x + yn-1)
If n is even (n = 2k)
xn + yn = (x + y)(xn-1 - xn-2y +...+ yn-2x - yn-1)
If n is odd (n = 2k + 1)
xn + yn = (x + y)(xn-1 - xn-2y +...- yn-2x + yn-1)
More Algebraic Formulas
2(a2 + b2) = (a + b)2 + (a - b)2
(a + b)2 - (a - b)2 = 4ab
(a - b)2 = (a + b)2 - 4ab
a4 + b4 = (a + b)(a - b)[(a + b)2 - 2ab]
✨HEY DEAR MATE ✨
⚡HERE IS YOUR SOLUTION ⚡
✌️HOPE IT HELPS U ✌️
Polynomial Identities
polynomial identities(short multiplication formulas):
(x + y)2 = x2 + 2xy + y2
(x - y)2 = x2 - 2xy + y2
polynomial identities(short multiplication formulas):
(x + y)2 = x2 + 2xy + y2
(x - y)2 = x2 - 2xy + y2
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2xz + 2yz
(x - y - z)2 = x2 + y2 + z2 - 2xy - 2xz + 2yz
Factor Rules
x2 - y2 = (x - y)(x + y)
x2 + y2 = (x + y)2 - 2xy
or
x2 + y2 = (x - y)2 + 2xy
If n is a natural number
xn - yn = (x - y)(xn-1 + xn-2y +...+ yn-2x + yn-1)
If n is even (n = 2k)
xn + yn = (x + y)(xn-1 - xn-2y +...+ yn-2x - yn-1)
If n is odd (n = 2k + 1)
xn + yn = (x + y)(xn-1 - xn-2y +...- yn-2x + yn-1)
More Algebraic Formulas
2(a2 + b2) = (a + b)2 + (a - b)2
(a + b)2 - (a - b)2 = 4ab
(a - b)2 = (a + b)2 - 4ab
a4 + b4 = (a + b)(a - b)[(a + b)2 - 2ab]
✨HEY DEAR MATE ✨
⚡HERE IS YOUR SOLUTION ⚡
✌️HOPE IT HELPS U ✌️
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