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Question

Find the product using appropriate identity:
(x+yz)(x2+y2+z2xy+yz+zx)

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Solution

We know the identity (a+b+c)(a2+b2+c2abbcca)=a3+b3+c33abc

Using the above identity taking a=x, b=y and c=z, the product (x+yz)(x2+y2+z2xy+yz+zx) can be computed as follows:

(x+yz)(x2+y2+z2xy+yz+zx)=x3+(y)3+(z)3(3x×y×z)=x3+y3z3+3xyz

Hence, (x+yz)(x2+y2+z2xy+yz+zx)=x3+y3z3+3xyz


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