Question

FACTORIZE 9a²-24ab+16b²-4c²​

Answer 1

$\huge {\mathfrak {\underline {\red {Given:}}}}$

$\large {9 {a}^{2} - 24ab + 16 {b}^{2} - 4 {c}^{2}}$

$\huge {\mathfrak {\underline {\green {Solution:}}}}$

$\large {9 {a}^{2} - 24ab + 16 {b}^{2} - 4 {c}^{2}}$

=⟩ $\large{ {(3a)}^{2} - (2 \times 3a \times 4b) + {(4b)}^{2} - {(2c)}^{2}}$ (the question can also be written in this way.)

=⟩ $\large { {(3a - 4b)}^{2} - {(2c)}^{2} }$ (by using the formula— $\large { {(a - b)}^{2} = {a}^{2} -2ab + {b}^{2} }$)

=⟩ $\large {(3a - 4b + 2c)(3a - 4b - 2c)}$ (by using formula— $\large {{a}^{2} - {b}^{2} = (a + b) (a - b)}$

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