Question

resolve into factor of 81m⁴-(n-m)⁴​

Answer 1

Step by Step Solution

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "m4" was replaced by "m^4".

STEP

1

:

Equation at the end of step 1

34m4 - m2

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

81m4 - m2 = m2 • (81m2 - 1)

Trying to factor as a Difference of Squares:

3.2 Factoring: 81m2 - 1

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 : 81 is the square of 9

Check : 1 is the square of 1

Check : m2 is the square of m1

Factorization is : (9m + 1) • (9m - 1)

Final result :

m2 • (9m + 1) • (9m - 1)