Question

Factorize 72-2b^2 using formula a^2-b^2.​

Answer 1

Answer:

2⋅(b+6)⋅(b−6)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 2b2 -  72

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  2b2 - 72  =   2 • (b2 - 36)  

Trying to factor as a Difference of Squares:

3.2      Factoring:  b2 - 36  

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 : 36 is the square of 6

Check :  b2  is the square of  b1  

Factorization is :       (b + 6)  •  (b - 6)