What is factor 2(x+y)^2+7x(x+y)+5x^2 ?

The solution to factor 2(x+y)^2+7x(x+y)+5x^2 is (7x+2y)(2x+y)

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factor 2(x+y)^2+7x(x+y)+5x^2

factor

2 (x + y)^{2} + 7 x (x + y) + 5 x^{2}

(7 x + 2 y) (2 x + y)

Solution steps

2 (x + y)^{2} + 7 x (x + y) + 5 x^{2}

(x + y)^{2} : x^{2} + 2 x y + y^{2}

= 2 (x^{2} + 2 x y + y^{2}) + 7 x (x + y) + 5 x^{2}

Expand

2 (x^{2} + 2 x y + y^{2}) : 2 x^{2} + 4 x y + 2 y^{2}

= 2 x^{2} + 4 x y + 2 y^{2} + 7 x (x + y) + 5 x^{2}

Expand

7 x (x + y) : 7 x^{2} + 7 x y

= 2 x^{2} + 4 x y + 2 y^{2} + 7 x^{2} + 7 x y + 5 x^{2}

Simplify

2 x^{2} + 4 x y + 2 y^{2} + 7 x^{2} + 7 x y + 5 x^{2} : 14 x^{2} + 11 x y + 2 y^{2}

= 14 x^{2} + 11 x y + 2 y^{2}

Break the expression into groups

= (14 x^{2} + 4 x y) + (7 x y + 2 y^{2})

Factor out

2 x

from

14 x^{2} + 4 x y : 2 x (7 x + 2 y)

Factor out

y

from

7 x y + 2 y^{2} : y (7 x + 2 y)

= 2 x (7 x + 2 y) + y (7 x + 2 y)

Factor out common term

7 x + 2 y

= (7 x + 2 y) (2 x + y)

- x^{2} + 36 \leq 0

240 x^{4} y^{3}

3 + (- 5)

220 + 2125

5 (7 - u) + 5 u \leq 33

What is factor 2(x+y)^2+7x(x+y)+5x^2 ?
The solution to factor 2(x+y)^2+7x(x+y)+5x^2 is (7x+2y)(2x+y)