Question

The factor of 2ax^2+4axy+3bx^2+2ay^2+6bxy^+3by^2

Answer 1

Answer:

$2ax^2+4axy+3bx^2+2ay^2+6bxy+3by^2= (x+y)^2(2a+3b)$

Explanation:

Given

$2ax^2+4axy+3bx^2+2ay^2+6bxy+3by^2$

Required

Factorize

$2ax^2+4axy+3bx^2+2ay^2+6bxy+3by^2$

Rewrite as:

$2ax^2+4axy+2ay^2+3bx^2+6bxy+3by^2$

Use square parenthesis

$[2ax^2+4axy+2ay^2]+[3bx^2+6bxy+3by^2]$

Expand each bracket

$[2ax^2+2axy+2axy+2ay^2]+[3bx^2+3bxy+3bxy+3by^2]$

Factorize each:

$[2ax(x+y) + 2ay(x+y)]+[3bx(x+y)+3by(x+y)]$

$[(2ax+2ay)(x+y)]+[(3bx+3by)(x+y)]$

Further, factorize:

$(x+y)[(2ax+2ay)]+[(3bx+3by)]$

$(x+y)[(2ax+2ay)+(3bx+3by)]$

Remove bracket

$(x+y)[2ax+2ay+3bx+3by]$

Reorder:

$(x+y)[2ax+3bx+2ay+3by]$

Factorize:

$(x+y)[x(2a+3b)+y(2a+3b)]$

$(x+y)[(x+y)(2a+3b)]$

Remove square bracket

$(x+y)(x+y)(2a+3b)$

This gives:

$(x+y)^2(2a+3b)$

Hence:

$2ax^2+4axy+3bx^2+2ay^2+6bxy+3by^2= (x+y)^2(2a+3b)$