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verify x3+y3=(x+y)(x2-xy+y2)
Most Upvoted Answer
verify x3+y3=(x+y)(x2-xy+y2)
Verification of x3y3 = (xy)(x2 - xy + y2)
- Start with the left-hand side of the equation: x3y3
- Use the rule of exponents to rewrite x3 as x2 * x and y3 as y2 * y
- Substitute these values into the equation: x2 * x * y2 * y
- Factor out xy from the product: xy * (x2 * y2)
- Use the identity a2 - b2 = (a + b)(a - b) to factor x2 - y2 as (x + y)(x - y)
- Substitute this value into the equation: xy * (x + y)(x - y)
- Use the distributive property to expand the product: xy * (x2 - xy + y2)
- Compare this expression to the right-hand side of the equation: (xy)(x2 - xy + y2)
- Since they are equal, the original equation x3y3 = (xy)(x2 - xy + y2) is verified.
Community Answer
verify x3+y3=(x+y)(x2-xy+y2)
L.H.S=x^3+y^3
=(x+y)^3 - 3xy(x+y)
Taking (x+y)common,
=(x+y) {(x+y)^2 - 3xy}
=(x+y) {x^2+y^2+2xy-3xy}
=(x+y) (x^2-xy+y^2)..
=R.H.S.
=(x+y)^3 - 3xy(x+y)
Taking (x+y)common,
=(x+y) {(x+y)^2 - 3xy}
=(x+y) {x^2+y^2+2xy-3xy}
=(x+y) (x^2-xy+y^2)..
=R.H.S.
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verify x3+y3=(x+y)(x2-xy+y2) for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about verify x3+y3=(x+y)(x2-xy+y2) covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for verify x3+y3=(x+y)(x2-xy+y2).
verify x3+y3=(x+y)(x2-xy+y2) for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about verify x3+y3=(x+y)(x2-xy+y2) covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for verify x3+y3=(x+y)(x2-xy+y2).
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