M=3a^2(a^2-5)+a(-3a^3+4a)+6a^2 with a=-5

Step-by-step explanation:

STEP 1: Equation at the end of step 1

(((3•( ))•(()-5))+(a•((0-)+4a)))+(2•3)

STEP 2:(((3•(a2))•((a2)-5))+(a•((0-3a3)+4a)))+(2•3a2)

Pulling out like terms

Pull out like factors :

  4a - 3a3  =   -a • (3a2 - 4)

Trying to factor as a Difference of Squares:

4.2      Factoring:  3a2 - 4

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

Multiplying exponential expressions :

4.3    a1 multiplied by a1 = a(1 + 1) = a2

Equation at the end of step

4

:

 (((3•(a2))•((a2)-5))+-a2•(3a2-4))+(2•3a2)

STEP

5

:

Equation at the end of step

5

:

 ((3a2 • (a2 - 5)) +  -a2 • (3a2 - 4)) +  (2•3a2)

STEP

6

:

Trying to factor as a Difference of Squares:

6.1      Factoring:  a2-5

Check : 5 is not a square !!

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

Equation at the end of step

6

:

 (3a2 • (a2 - 5) +  -a2 • (3a2 - 4)) +  (2•3a2)'

STEP

7

:

Final result :

 -5a2

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