Question

what is the common factors of 2a^2b^3, 8a^3b^2, 12a^2b^2​

Answer 1

Answer:

:

Equation at the end of step 1

((((8•(a3))•b)-((20•(a2))•(b2)))-(12a•(b3))) (12ab-(6•(b2)))

————————————————————————————————————————————•———————————————

((8•(a2))-2ab) (22a2-b2)

STEP

2

:

Equation at the end of step

2

:

((((8•(a3))•b)-((20•(a2))•(b2)))-(12a•(b3))) (12ab-(2•3b2))

————————————————————————————————————————————•——————————————

((8•(a2))-2ab) (4a2-b2)

STEP

3

:

12ab - 6b2

Simplify ——————————

4a2 - b2

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

12ab - 6b2 = 6b • (2a - b)

Trying to factor as a Difference of Squares:

4.2 Factoring: 4a2 - b2

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 : 4 is the square of 2

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (2a + b) • (2a - b)

Canceling Out :

4.3 Cancel out (2a - b) which appears on both sides of the fraction line.

Equation at the end of step

4

:

((((8•(a3))•b)-((20•(a2))•(b2)))-(12a•(b3))) 6b

————————————————————————————————————————————•————

((8•(a2))-2ab) 2a+b

STEP

5

:

Equation at the end of step

5

:

((((8•(a3))•b)-((20•(a2))•(b2)))-(12a•(b3))) 6b

————————————————————————————————————————————•————

(23a2-2ab) 2a+b

STEP

6

:

Equation at the end of step

6

:

((((8•(a3))•b)-((20•(a2))•(b2)))-(22•3ab3)) 6b

———————————————————————————————————————————•————

(8a2-2ab) 2a+b

STEP

7

:

Equation at the end of step

7

:

((((8•(a3))•b)-((22•5a2)•b2))-(22•3ab3)) 6b

————————————————————————————————————————•————

(8a2-2ab) 2a+b

STEP

8

:

Equation at the end of step

8

:

(((23a3•b)-(22•5a2b2))-(22•3ab3)) 6b

—————————————————————————————————•————

(8a2-2ab) 2a+b

STEP

9

:

8a3b - 20a2b2 - 12ab3

Simplify —————————————————————

8a2 - 2ab

STEP

10

:

Pulling out like terms

10.1 Pull out like factors :

8a3b - 20a2b2 - 12ab3 = 4ab • (2a2 - 5ab - 3b2)

STEP

11

:

Pulling out like terms

11.1 Pull out like factors :

8a2 - 2ab = 2a • (4a - b)

Trying to factor a multi variable polynomial :

11.2 Factoring 2a2 - 5ab - 3b2

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