Question

10a2 - 15ab/
6ab-9b2​

Answer 1

(1): "b2" was replaced by "b^2". 2 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

STEP

2

:

Equation at the end of step

2

:

STEP

3

:

Equation at the end of step

3

:

STEP

4

:

10a2 - 15ab

Simplify ———————————

4a2 - 9b2

STEP

5

:

Pulling out like terms

5.1 Pull out like factors :

10a2 - 15ab = 5a • (2a - 3b)

Trying to factor as a Difference of Squares:

5.2 Factoring: 4a2 - 9b2

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 : 9 is the square of 3

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (2a + 3b) • (2a - 3b)

Canceling Out :

5.3 Cancel out (2a - 3b) which appears on both sides of the fraction line.

Final result :

5a

———————

2a + 3b

Answer 2

QUESTION:

10a²-15ab+6ab-9b²

SOLUTION:

☞5a(2a-3b)+3b(2a-3b)

☞(5a+3b)(2a-3b)

ANSWER:

✿(5a+3b)(2a-3b)✿