Rojean47idn
Answered

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factor completely

32m³ - 50m

tysm po sa sasagot! God bless you all po​

Sagot :

Maglapayevaidn

Answer:

2m • (5m + 4) • (5m - 4)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

(2•52m3) - 32m

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

50m3 - 32m = 2m • (25m2 - 16)

Trying to factor as a Difference of Squares:

3.2 Factoring: 25m2 - 16

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 : 25 is the square of 5

Check : 16 is the square of 4

Check : m2 is the square of m1

Factorization is : (5m + 4) • (5m - 4)

Final result :

2m • (5m + 4) • (5m - 4)