Factorize:
$a^{2} + 6 a + 9 - 4 b^{2}$

$(a + 2 b + 3) (a - 2 b + 3)$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$(a + 3 + 2 b) (a + 3 - 2 b)$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$(a - 3 + 2 b) (a + 3 - 2 b)$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$(a + 3 + 2 b) (a - 3 - 2 b)$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct options are
A
$(a + 2 b + 3) (a - 2 b + 3)$

B
$(a + 3 + 2 b) (a + 3 - 2 b)$

$\Rightarrow a^{2} + 6 a + 9 - 4 b^{2}$

$= (a^{2} + 6 a + 9) - (4 b^{2})$

$= (a^{2} + 3 a + 3 a + 9) - (4 b^{2})$

$= (a (a + 3) + 3 (a + 3) - (4 b^{2})$

$= [(a + 3) (a + 3) - (4 b^{2})]$

$= [(a + 3)^{2} - (4 b^{2})]$

$= [(a + 3)^{2} - (2 b)^{2}]$

$L e t (a + 3) = x a n d 2 b = y$

$\Rightarrow [x^{2} - y^{2}] = (x + y) (x - y)$

$Subtituting the values back we get$

$(a + 3 + 2 b) (a + 3 - 2 b)$

Suggest Corrections