Question

( 7a square - 63b square )

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

 (7 • (a2)) -  (32•7b2)

STEP  

2

:

Equation at the end of step

2

:

 7a2 -  (32•7b2)

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  7a2 - 63b2  =   7 • (a2 - 9b2)  

Trying to factor as a Difference of Squares:

4.2      Factoring:  a2 - 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 : 9 is the square of 3

Check :  a2  is the square of  a1  

Check :  b2  is the square of  b1  

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

Final result :

 7 • (a + 3b) • (a - 3b)

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