Question

Factorise 343x5+27x2y3 +441x4y+189x3y2

Answer 1

$Let \: p(x) = 343x^{5}+27x^{2}y^{3}+441x^{4}y+189x^{3}y^{2}$

$= x^{2} (343x^{3}+27y^{3}+441x^{2}y+189xy^{2})\\= x^{2}[(7x)^{3} + (3y)^{3} + 3\times(7x)^{2}y+3\times (7x)\times (3y)^{2} ] \\= x^{2}(7x+3y)^{3}$

/* By Algebraic Identity */

$\boxed {\pink {a^{3}+b^{3}+3a^{2}b+3ab^{2} = (a+b)^{3} }}$

$= x^{2} (7x+3y)(7x+3y)(7x+3y)$

Therefore.,

$\red{ Factors \:of \:343x^{5}+27x^{2}y^{3}+441x^{4}y+189x^{3}y^{2}}$

$\green {= x^{2} (7x+3y)(7x+3y)(7x+3y)}$

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