Question

Factorize 9xsquarey-24xysquare+16y

Answer 1

Correct Question:

$9x^{2} - 24xy + 16y^{2}$

To Find:

Factorization of the equation.

Identity Used:

• $\big(a - b)^{2}\big) = a^{2} - 2ab + b^{2}$
• By middle-splitting theorem

Solution:

$9x^{2} - 24xy + 16y^{2}$

$9x^{2} - 12xy - 12xy + 16y^{2}$

$3x(3x - 4y) - 4(3x - 4y)$

$(3x - 4y) (3x - 4y)$

$(3x - 4y)^{2}$

Answer 2

$\sf{\huge{\purple{\mathfrak{\underline{\underline{Question}}}}}}$

$\sf Factorise \\ 9x^2y - 24xy^2 + 16y^3$

$\sf{\huge{\purple{\mathfrak{\underline{\underline{Solution}}}}}}$

$\sf \implies 9x^2y - 24xy^2+ 16y^3 \\ \implies \sf y( (3x)^2 - 2\times 3x \times 4y + (4y)^2)$

$\sf{\bold{\red{\boxed{x^2 - 2xy + y^2 = (x-y)^2}}}}$

$\sf\implies y(3x - 4y)^2$

$\sf{\bold{\red{\boxed{y(3x - 4y)^2}}}}$

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$\sf{\huge{\orange{\mathfrak{\underline{Extra\:information}}}}}$

• $(x+y)^2 = x^2 + y^2 + 2xy$
• $(x-y)^2 = x^2 + y^2 - 2xy$
• $(x+y)(x-y) = x^2 - y^2$

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