The expression m3 + n3 + 3mn2? + 3m’n2 is equal to
Answers
Answer:
m3 +6mn2 + n3
Is the answer
Step-by-step explanation:
Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): "n2" was replaced by "n^2". 3 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
(((m3)-(n3))-(m•((m2)-(n2))))+n•(m-n)3
STEP
2
:
Evaluate an expression:
2.1 Factoring: m2-n2
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 : m2 is the square of m1
Check : n2 is the square of n1
Factorization is : (m + n) • (m - n)
Equation at the end of step
2
:
(((m3)-(n3))-m•(m+n)•(m-n))+n•(m-n)3
STEP
3
:
3.1 Evaluate : (m-n)3 = m3-3m2n+3mn2-n3
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
m3n - 3m2n2 + 3mn3 + mn2 - n4 - n3 =
n • (m3 - 3m2n + 3mn2 + mn - n3 - n2)
Trying to factor by pulling out :
4.2 Factoring: m3 - 3m2n + 3mn2 + mn - n3 - n2
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -n3 - n2
Group 2: -3m2n + 3mn2
Group 3: m3 + mn
Pull out from each group separately :
Group 1: (n + 1) • (-n2)
Group 2: (m - n) • (-3mn)
Group 3: (m2 + n) • (m)
Looking for common sub-expressions :
Group 1: (n + 1) • (-n2)
Group 3: (m2 + n) • (m)
Group 2: (m - n) • (-3mn)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Final result :
n • (m3 - 3m2n + 3mn2 + mn - n3 - n2)