Advertisements
Advertisements
प्रश्न
Factorize x4 + x2 y2 + y4
Advertisements
उत्तर
Adding x2 y2 and subtracting x2 y2 to the given equation.
= x4 + x2 y2 + y4 + x2 y2 - x2 y2
= x4 + 2x2 y2 + y4 - x2 y2
= (x2 )2 + 2 x x2 x y2 + ( y2 )2 - ( xy)2
Using identity a2 + 2ab + b2 = (a + b)2
= (x2 + y2 )2 - ( xy)2
Using identity a2 - b2 = (a + b)(a - b)
= (x2 + y2 + xy)(x2 + y2 - xy )
∴ x4 + x2 y2 + y4 = (x2 + y2 + xy)(x2 + y2 - xy)
APPEARS IN
संबंधित प्रश्न
Get the algebraic expression in the following case using variables, constants and arithmetic operations.
One-fourth of the product of numbers p and q.
Get the algebraic expression in the following case using variables, constants and arithmetic operations.
Sum of numbers a and b subtracted from their product.
Factorize `[x^2 + 1/x^2] - 4[x + 1/x] + 6`
Factorize the following expressions:
( x + 2)3 + ( x - 2)3
The expression (a − b)3 + (b − c)3 + (c −a)3 can be factorized as
Divide: 12a2 + ax - 6x2 by 3a - 2x
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 ______.
If x = 2 and y = 3, then find the value of the following expressions
x + y
A triangle is made up of 2 red sticks and 1 blue sticks 
. The length of a red stick is given by r and that of a blue stick is given by b. Using this information, write an expression for the total length of sticks in the pattern given below:
