Question

Fatorize: 2(x+y)²-7(x+y)+6​

Answer 1

Answer:

We have, \sf{(x-y)^2-7(x^2-y^2)+12(x+y)^2}(x−y)

2

−7(x

2

−y

2

)+12(x+y)

2

=\sf{(x-y)^2-7(x-y)(x+y)+12(x+y)^2}(x−y)

2

−7(x−y)(x+y)+12(x+y)

2

= \sf{a^2-7ab+12b^2,}a

2

−7ab+12b

2

, where x-y = a and x + y = b

= \sf{a^2-3ab-4ab+12b^2}a

2

−3ab−4ab+12b

2

=\sf{(a^2-3ab)+[-4ab+12b^2]}(a

2

−3ab)+[−4ab+12b

2

]

= \sf{a(a-3b)-4b(a-3b)}a(a−3b)−4b(a−3b)

=\sf{(a-3b)(a-4b)}(a−3b)(a−4b)

= [(x-y) - 3(x+y)] [(x-y)-4(x+y)], putting back a = x-y and b =x+y

= \sf{[x-y-3x-3y][x-y-4x-4y]}[x−y−3x−3y][x−y−4x−4y]

= \sf{(-2x-4y)-(-3x-5y)}(−2x−4y)−(−3x−5y)

=\sf{[-(2x+4y)][-(3x+5y)]}[−(2x+4y)][−(3x+5y)]

=\sf{(2x+4y)(3x+5y)}(2x+4y)(3x+5y)

\bold{\large{\boxed{\sf{\red{2(x+2y)(3x+5y)}}}}}

2(x+2y)(3x+5y)

Answer 2

Answer:

2x²+4xy+2y²-7x-7y+6