Question

por favor ayudenme no le entiendo. (3x^2+2y)(3x^2+2y)(3x^2+2y)=​

Answer 1

((3 • (x2)) - 2y) • (2y - 3x2)
STEP
2
:

Equation at the end of step
2
:

(3x2 - 2y) • (2y - 3x2)
STEP
3
:

Trying to factor as a Difference of Squares:

3.1 Factoring: 3x2-2y

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

Trying to factor as a Difference of Squares:

3.2 Factoring: 2y-3x2

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the
difference of two perfect squares

3.3 Rewrite (2y-3x2) as (-1) • (3x2-2y)
Multiplying Exponential Expressions:

3.4 Multiply (3x2-2y) by (3x2-2y)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (3x2-2y) and the exponents are :
1 , as (3x2-2y) is the same number as (3x2-2y)1
and 1 , as (3x2-2y) is the same number as (3x2-2y)1
The product is therefore, (3x2-2y)(1+1) = (3x2-2y)2


Final result :
(3x2 - 2y)2 • -1