Question

factorise
40(3x+4y)^2 + 14(3x+4y) +1

Answer 1

Answer:

please check the attached image.

Answer 2

The factorisation of $40(3x+4y)^2+14(3x+4y)+1$ is $(30x+40y+1)(12x+16y+1).$

Step-by-step explanation:

We have,

$40(3x+4y)^2+14(3x+4y)+1$      .....(1)

To find, the factorisation of $40(3x+4y)^2+14(3x+4y)+1=?$

Let $3x+4y=p$

Now, (1) can be written as

∴ $40p^2+14p+1$

$=40p^2+10p+4p+1$

$=10p(4p+1)+1(4p+1)$

$=(10p+1)(4p+1)$    .....(2)

Put $3x+4y=p$in (2), we get

$=(10(3x+4y)+1)(4(3x+4y)+1)$

$=(30x+40y+1)(12x+16y+1)$

Hence, the factorisation of $40(3x+4y)^2+14(3x+4y)+1$ is $(30x+40y+1)(12x+16y+1).$