Advertisements
Advertisements
Question
Factorize xy9 - yx9
Solution
xy9 - yx9
= xy ( y8 - x8 )
= xy (( y4)2 - (x4 )2 )
Using identity a2 - b2 = (a + b)(a - b)
= xy ( y4 + x4 )( y4 - x4 )
= xy ( y4 + x4 )(( y2)2 - (x2 )2 )
Using identity a2 - b2 = (a + b)(a - b)
= xy ( y4 + x4 )( y2 + x2 )( y2 - x2 )
= xy ( y4 + x4 )( y2 + x2 )( y + x)( y - x)
= xy (x4 + y4 )(x2 + y2 )( x + y )(-1)( x - y )
∵ (b - a) = -1(a - b)
= -xy (x4 + y4 )(x2 + y2 )( x + y )( x - y )
∴ xy9 - yx9 = -xy (x4 + y4 )(x2 + y2 )(x + y )(x - y )
APPEARS IN
RELATED QUESTIONS
Factorize a3 – 3a2b + 3ab2 – b3 + 8
Simplify : \[\frac{1 . 2 \times 1 . 2 \times 1 . 2 - 0 . 2 \times 0 . 2 \times 0 . 2}{1 . 2 \times 1 . 2 + 1 . 2 \times 0 . 2 + 0 . 2 \times 0 . 2}\]
27x3 − y3 − z3 − 9xyz
The value of \[\frac{(2 . 3 )^3 - 0 . 027}{(2 . 3 )^2 + 0 . 69 + 0 . 09}\]
Multiply: (2x - 3y)(2x + 3y)
Write in the form of an algebraic expression:
Perimeter (P) of a square is four times its side.
The solution of the equation `"3x" - 1/2 = 5/2 + "x"` is ______.
Write the coefficient of x2 and x in the following polynomials
πx2 – x + 2
The variable in the expression 16x – 7 is __________
Write the variables, constant and terms of the following expression
18 + x – y
