Question

Factorise 15x3y2z- 25xy2z3

Answer 1

Answer:

5xy2z⋅(3x2−5z2)

Step-by-step explanation:

Step 1 :Equation at the end of step 1

(((15•(x3))•(y2))•z)-(52xy2•z3)

Step 2 : Equation at the end of step 2 :

(((3•5x3) • y2) • z) -  52xy2z3

Step 3 :Pulling out like terms

Pull out like factors :

15x3y2z - 25xy2z3  =   5xy2z • (3x2 - 5z2)

Trying to factor as a Difference of Squares:

Factoring:  3x2 - 5z2

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

Final result : 5xy2z • (3x2 - 5z2)

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Answer 2

The solution is on the above attachment. plss check .