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If x+y=-4 and x-y=2, what is the value of (x+y)(x^(2)-y^(2)) ?

If x+y=−4 x+y=-4 and x−y=2 x-y=2 , what is the value of (x+y)(x2−y2)? (x+y)\left(x^{2}-y^{2}\right) ?

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Full solution

Q. If x+y=−4 x+y=-4 and x−y=2 x-y=2 , what is the value of (x+y)(x2−y2)? (x+y)\left(x^{2}-y^{2}\right) ?
  1. Add Equations: Add the two equations together to find the value of xx.(x+y)+(x−y)=−4+2(x+y) + (x-y) = -4 + 22x=−22x = -2x=−1x = -1
  2. Substitute xx: Substitute xx back into one of the original equations to find yy.\newline−1+y=−4-1 + y = -4\newliney=−3y = -3
  3. Substitute values: Now substitute the values of xx and yy into the expression (x+y)(x2−y2)(x+y)(x^{2}-y^{2}).\(\newline\)(−1−3)((−1)2−(−3)2)(-1-3)((-1)^{2}-(-3)^{2})
  4. Simplify expression: Simplify the expression. (−4)(1−9)(-4)(1-9)
  5. Continue simplifying: Continue simplifying.\newline(−4)(−8)(-4)(-8)
  6. Calculate result: Calculate the final result. 3232

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