Factorise:
$x^{2} + 2 x - (4 a^{2} + 8 a + 3)$

{x + (2 a + 3)} {x - (2 a + 1)}

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

{x + (2 a - 3)} {x - (2 a + 1)}

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

{x - (2 a + 3)} {x - (2 a + 1)}

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

{x + (2 a + 3)} {x - (2 a - 1)}

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

Open in App

Solution

The correct option is A ${x + (2 a + 3)} {x - (2 a + 1)}$
We have to factorise:
$x^{2} + 2 x - (4 a^{2} + 8 a + 3)$

$4 a^{2} + 8 a + 3$ can be written as
$4 a^{2} + 8 a + 3 = 4 a^{2} + (2 + 6) a + 3$
$= 4 a^{2} + 2 a + 6 a + 3$
$= 2 a (2 a + 1) + 3 (2 a + 1)$
$= (2 a + 1) (2 a + 3)$

$(2 a + 1) + (2 a + 3) = 4 a + 4$
$(2 a + 3) - (2 a + 1) = 2 a + 3 - 2 a - 1 = 2$
$x^{2} + 2 x - (4 a^{2} + 8 a + 3)$
$= x^{2} + {(2 a + 3) - (2 a + 1)} x - (2 a + 3) (2 a + 1)$
$= x^{2} + (2 a + 3) x - (2 a + 1) x - (2 a + 3) (2 a + 1)$
$= x {x + (2 a + 3)} - (2 a + 1) {x + (2 a + 3)}$
$= {x + (2 a + 3)} {x - (2 a + 1)}$
Hence, the answer is (a)

Suggest Corrections