Question

factorise 8(a+b)²+14(a+b)+3​

Answer 1

$Given \: 8(a+b)^{2} + 14(a+b) + 3$

/* Splitting the middle term, we get */

$= 8(a+b)^{2} + 12(a+b) + 2(a+b) + 3$

$= 4(a+b)[ 2(a+b)+3] + 1[ 2(a+b) + 3 ]$

$= [2(a+b) + 3 ][ 4(a+b)+1]$

$= ( 2a+2b+3)(4a+4b+1)$

Therefore.,

$\red{ Factors \:of \:8(a+b)^{2} + 14(a+b) + 3}$

$\green { = ( 2a+2b+3)(4a+4b+1) }$

•••♪

Answer 2

Question :-

Factorise 8(a+b)²+ 14(a+b) + 3

Answer :-

Let a + b = x.

Then, 8(a + b)² + 14(a + b) + 3 = 8x² + 14x + 3.

We have to find two numbers such that their products is 8 × 3 = 24 and their sum is 14.

We find that 12 × 2 = 24 and 12 + 2 = 14

Therefore,

8x² + 14x + 3 = 8x² + 12x + 2x + 3

→ 4x(2x + 3) + 1(2x + 3)

→ (2x + 3)(4x + 1)

→ {2(a + b) + 3}{4 (a + b) + 1}

→ (2a + 2b + 3)(4a + 4b + 1).

_______________________

Hope my solution helps you :)

#BeBrainly