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Question
Multiply: x2 + y2 + z2 − xy + xz + yz by x + y − z
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Solution
The given expression is
`x^2 +y^2 +z^2 - xy +xz + yz`
We have to multiply the above expression by `(x+y-y)`.
The required product is
`(x+y-z)(x^2 + y^2 +z^2 -xy +xz +yz)`
`= {x+y + (-z)} {(x)^2 + (y^2) + (-z)^2 =- x,y-y (-z) - (-z).x}`
Recall the formula
`a^3 +b^3 +c^3 -3abc = (a+b+c)(a^2+b^2+c^2 - ab - bc -ca)`
Using the above formula, we have
`=x^3 + y^3 + ( -z)^3 -3 .x.y.(-z)`
` = x^3 +y^3 - z^3 +3xyz`
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