Question

factorise
10xy+3 -15x-2y
​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

(10x • (y3)) - (2•5x4)

STEP

2

:

Equation at the end of step

2

:

(2•5xy3) - (2•5x4)

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

10xy3 - 10x4 = -10x • (x3 - y3)

Trying to factor as a Difference of Cubes:

4.2 Factoring: x3 - y3

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0-b3 =

a3-b3

Check : x3 is the cube of x1

Check : y3 is the cube of y1

Factorization is :

(x - y) • (x2 + xy + y2)

Trying to factor a multi variable polynomial :

4.3 Factoring x2 + xy + y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

-10x • (x - y) • (x2 + xy + y2)