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प्रश्न
(x + y)3 − (x − y)3 can be factorized as
पर्याय
2y (3x2 + y2)
2x (3x2 + y2)
2y (3y2 + x2)
2x (x2+ 3y2)
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उत्तर
The given expression to be factorized is
(x + y)3 − (x − y)3
Recall the formula for difference of two cubes `a^3 -b^3 = (a-b)(a^2 +ab +b^2)`
Using the above formula, we have,
`(x+y)^3 - (x-y)^3`
` = {(x+y) - (x-y)} {(x+y)^2 + (x+y).(x-y) + (x-y)^3}`
` = (x+y - x +y)[{(x)^2 + 2x.y + (y)^2} + (x^2 -y^2) + {x^2 -y^2}+{(x)^2 -2x.y +(y)^2}]`
` = 2y(x^2 + 2 xy + y^2 +x^2 - y^2 +x^2 - 2xy + y^2)`
` = 2y (3x^2 + y^2)`
The given expression to be factorized is
(x + y)3 − (x − y)3
Recall the formula for difference of two cubes `a^3 -b^3 = (a-b)(a^2 +ab +b^2)`
Using the above formula, we have,
= (x + y)3 − (x − y)3
= `{(x+y) - (x-y)}{(x+y)^2 + (x+y).(x-y)+ (x-y)^2}`
`= (x+y - x+y)[{(x)^2 + 2x.y + (y)^2} + (x^2 - y^2)+ {(x)^2 - 2.x.y + (y^2)}]`
`=2y (x^2 + 2xy + y^2 +x^2 - y^2 + x^2 - 2xy +y^2)`
` = 2y (3x^2 + y^2)`
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