Resolve into factors: 81 x^{2} y^{2}+108 x y | vedclass

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Question

(C) The given expression is $81 x^{2} y^{2}+108 x y z+36 z^{2}$.We can rewrite this expression in the form of the algebraic identity $(a+b)^{2} = a^{2

Vedclass · Accepted Answer

$(9 x y+6 z)^{2}$

Vedclass · Answer

(C) The given expression is $81 x^{2} y^{2}+108 x y z+36 z^{2}$.We can rewrite this expression in the form of the algebraic identity $(a+b)^{2} = a^{2}+2ab+b^{2}$.Here,$a^{2} = (9 x y)^{2}$ and $b^{2} = (6 z)^{2}$.Thus,$a = 9 x y$ and $b = 6 z$.Now,check the middle term: $2ab = 2(9 x y)(6 z) = 108 x y z$.Since the expression matches the identity,we have:$81 x^{2} y^{2}+108 x y z+36 z^{2} = (9 x y+6 z)^{2}$.

Resolve into factors: $81 x^{2} y^{2}+108 x y z+36 z^{2}$.

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