Factorise: 2x^2 + y^2 + 8z^2 - 2sqrt{2}xy + 4 | vedclass

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Question

(A) The given expression is $2x^2 + y^2 + 8z^2 - 2\sqrt{2}xy + 4\sqrt{2}yz - 8xz$.We use the algebraic identity: $(a + b + c)^2 = a^2 + b^2 + c^2 + 2a

Vedclass · Accepted Answer

$(-\sqrt{2}x + y + 2\sqrt{2}z)^2$

Vedclass · Answer

(A) The given expression is $2x^2 + y^2 + 8z^2 - 2\sqrt{2}xy + 4\sqrt{2}yz - 8xz$.We use the algebraic identity: $(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$.We can rewrite the expression as:$(-\sqrt{2}x)^2 + (y)^2 + (2\sqrt{2}z)^2 + 2(-\sqrt{2}x)(y) + 2(y)(2\sqrt{2}z) + 2(2\sqrt{2}z)(-\sqrt{2}x)$Here,$a = -\sqrt{2}x$,$b = y$,and $c = 2\sqrt{2}z$.Thus,the expression becomes $(-\sqrt{2}x + y + 2\sqrt{2}z)^2$ or $(y - \sqrt{2}x + 2\sqrt{2}z)^2$.

Factorise: $2x^2 + y^2 + 8z^2 - 2\sqrt{2}xy + 4\sqrt{2}yz - 8xz$

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