What is factor ax-bx+cx+ay^2-by^2+cy^2 ?

The solution to factor ax-bx+cx+ay^2-by^2+cy^2 is (y^2+x)(a-b+c)

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factor ax-bx+cx+ay^2-by^2+cy^2

factor

a x - b x + c x + a y^{2} - b y^{2} + c y^{2}

(y^{2} + x) (a - b + c)

Solution steps

a x - b x + c x + a y^{2} - b y^{2} + c y^{2}

Factor out common term

a

= a (x + y^{2}) - b x + c x - b y^{2} + c y^{2}

Factor out common term

b

= a (y^{2} + x) - b (x + y^{2}) + c x + c y^{2}

Factor out common term

(y^{2} + x)

= (y^{2} + x) (a - b) + c x + c y^{2}

Factor out common term

c

= (y^{2} + x) (a - b) + c (x + y^{2})

Rewrite as

= (y^{2} + x) (a - b) + (y^{2} + x) c

Factor out common term

(y^{2} + x)

= (y^{2} + x) (a - b + c)

(x - 0.4 x) - 0.3 (x - 0.4 x)

(2 + 23 i)^{\frac{1}{3}}

9^{\frac{5}{6}}

\frac{315 + 5 1409}{32}

sin (t) (a t)

What is factor ax-bx+cx+ay^2-by^2+cy^2 ?
The solution to factor ax-bx+cx+ay^2-by^2+cy^2 is (y^2+x)(a-b+c)