Question

Simplify: 2y(3x^2-2x+y^2)– 3x (3y^2– 4x).

Answer 1

Answer:

2y3 - 9y2x + 6yx2 - 4yx + 12x2

Step-by-step explanation:

Step 1 :

Equation at the end of step 1 :

(2y•(((3•(x2))-2x)+(y2)))-(3x•(3y2-4x))

Step 2 :

Trying to factor as a Difference of Squares :

2.1 Factoring: 3y2-4x

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 3 is not a square !!

Ruling : Binomial can not be factored as the

difference of two perfect squares

Equation at the end of step 2 :

(2y•(((3•(x2))-2x)+(y2)))-3x•(3y2-4x)

Step 3 :

Equation at the end of step 3 :

(2y • ((3x2 - 2x) + y2)) - 3x • (3y2 - 4x)

Step 4 :

Trying to factor a multi variable polynomial :

4.1 Factoring y2 + 3x2 - 2x

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

Factorization fails

Equation at the end of step 4 :

2y • (y2 + 3x2 - 2x) - 3x • (3y2 - 4x)

Step 5 :

Final result :

2y3 - 9y2x + 6yx2 - 4yx + 12x2

Processing ends successfully

Answer 2

Answer:

[(2y+x)2(2y-x)] + [(2x+y)2(2x-y)]

[(4y2+x2+4xy)(2y-x)] + [(4x2+y2+4xy)(2x-y)]

[8y3+2x2y+8xy2-4xy2-x3-4x2y] + [8x3+2xy2+8x2y-4x2y-y3-4xy2]

[8y3-x3-2x2y+4xy2] + [8x3-y3-2xy2+4x2y]

8y3 - y3 + 8x3 - x3 + 2xy2 + 2x2y

7y3 +7x3 + 2xy(x+y)

7(x3 + y3) + 2xy(x+y)

(7)(x + y)(x2 + y2 - xy) + 2xy(x + y)

(7)(x+y)(x2 + y2 - xy + 2xy)

(7)(x + y)(x2 + y2 + xy)