Factor (a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3

Math
(a2-b2)3+(b2-c2)3+(c2-a2)3
Use the Binomial Theorem.
(a2)3+3(a2)2(-b2)+3a2(-b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
Simplify each term.
Tap for more steps…
Multiply the exponents in (a2)3.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a2⋅3+3(a2)2(-b2)+3a2(-b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
Multiply 2 by 3.
a6+3(a2)2(-b2)+3a2(-b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
a6+3(a2)2(-b2)+3a2(-b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
Rewrite using the commutative property of multiplication.
a6+3⋅-1(a2)2b2+3a2(-b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
Multiply 3 by -1.
a6-3(a2)2b2+3a2(-b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
Multiply the exponents in (a2)2.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a6-3a2⋅2b2+3a2(-b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
Multiply 2 by 2.
a6-3a4b2+3a2(-b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
a6-3a4b2+3a2(-b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
Apply the product rule to -b2.
a6-3a4b2+3a2((-1)2(b2)2)+(-b2)3+(b2-c2)3+(c2-a2)3
Rewrite using the commutative property of multiplication.
a6-3a4b2+3⋅(-1)2a2(b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
Raise -1 to the power of 2.
a6-3a4b2+3⋅1a2(b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
Multiply 3 by 1.
a6-3a4b2+3a2(b2)2+(-b2)3+(b2-c2)3+(c2-a2)3
Multiply the exponents in (b2)2.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a6-3a4b2+3a2b2⋅2+(-b2)3+(b2-c2)3+(c2-a2)3
Multiply 2 by 2.
a6-3a4b2+3a2b4+(-b2)3+(b2-c2)3+(c2-a2)3
a6-3a4b2+3a2b4+(-b2)3+(b2-c2)3+(c2-a2)3
Apply the product rule to -b2.
a6-3a4b2+3a2b4+(-1)3(b2)3+(b2-c2)3+(c2-a2)3
Raise -1 to the power of 3.
a6-3a4b2+3a2b4-(b2)3+(b2-c2)3+(c2-a2)3
Multiply the exponents in (b2)3.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a6-3a4b2+3a2b4-b2⋅3+(b2-c2)3+(c2-a2)3
Multiply 2 by 3.
a6-3a4b2+3a2b4-b6+(b2-c2)3+(c2-a2)3
a6-3a4b2+3a2b4-b6+(b2-c2)3+(c2-a2)3
a6-3a4b2+3a2b4-b6+(b2-c2)3+(c2-a2)3
Use the Binomial Theorem.
a6-3a4b2+3a2b4-b6+(b2)3+3(b2)2(-c2)+3b2(-c2)2+(-c2)3+(c2-a2)3
Simplify each term.
Tap for more steps…
Multiply the exponents in (b2)3.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a6-3a4b2+3a2b4-b6+b2⋅3+3(b2)2(-c2)+3b2(-c2)2+(-c2)3+(c2-a2)3
Multiply 2 by 3.
a6-3a4b2+3a2b4-b6+b6+3(b2)2(-c2)+3b2(-c2)2+(-c2)3+(c2-a2)3
a6-3a4b2+3a2b4-b6+b6+3(b2)2(-c2)+3b2(-c2)2+(-c2)3+(c2-a2)3
Rewrite using the commutative property of multiplication.
a6-3a4b2+3a2b4-b6+b6+3⋅-1(b2)2c2+3b2(-c2)2+(-c2)3+(c2-a2)3
Multiply 3 by -1.
a6-3a4b2+3a2b4-b6+b6-3(b2)2c2+3b2(-c2)2+(-c2)3+(c2-a2)3
Multiply the exponents in (b2)2.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a6-3a4b2+3a2b4-b6+b6-3b2⋅2c2+3b2(-c2)2+(-c2)3+(c2-a2)3
Multiply 2 by 2.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2(-c2)2+(-c2)3+(c2-a2)3
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2(-c2)2+(-c2)3+(c2-a2)3
Apply the product rule to -c2.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2((-1)2(c2)2)+(-c2)3+(c2-a2)3
Rewrite using the commutative property of multiplication.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3⋅(-1)2b2(c2)2+(-c2)3+(c2-a2)3
Raise -1 to the power of 2.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3⋅1b2(c2)2+(-c2)3+(c2-a2)3
Multiply 3 by 1.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2(c2)2+(-c2)3+(c2-a2)3
Multiply the exponents in (c2)2.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c2⋅2+(-c2)3+(c2-a2)3
Multiply 2 by 2.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4+(-c2)3+(c2-a2)3
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4+(-c2)3+(c2-a2)3
Apply the product rule to -c2.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4+(-1)3(c2)3+(c2-a2)3
Raise -1 to the power of 3.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-(c2)3+(c2-a2)3
Multiply the exponents in (c2)3.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c2⋅3+(c2-a2)3
Multiply 2 by 3.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+(c2-a2)3
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+(c2-a2)3
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+(c2-a2)3
Use the Binomial Theorem.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+(c2)3+3(c2)2(-a2)+3c2(-a2)2+(-a2)3
Simplify each term.
Tap for more steps…
Multiply the exponents in (c2)3.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c2⋅3+3(c2)2(-a2)+3c2(-a2)2+(-a2)3
Multiply 2 by 3.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6+3(c2)2(-a2)+3c2(-a2)2+(-a2)3
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6+3(c2)2(-a2)+3c2(-a2)2+(-a2)3
Rewrite using the commutative property of multiplication.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6+3⋅-1(c2)2a2+3c2(-a2)2+(-a2)3
Multiply 3 by -1.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3(c2)2a2+3c2(-a2)2+(-a2)3
Multiply the exponents in (c2)2.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c2⋅2a2+3c2(-a2)2+(-a2)3
Multiply 2 by 2.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2(-a2)2+(-a2)3
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2(-a2)2+(-a2)3
Apply the product rule to -a2.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2((-1)2(a2)2)+(-a2)3
Rewrite using the commutative property of multiplication.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3⋅(-1)2c2(a2)2+(-a2)3
Raise -1 to the power of 2.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3⋅1c2(a2)2+(-a2)3
Multiply 3 by 1.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2(a2)2+(-a2)3
Multiply the exponents in (a2)2.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a2⋅2+(-a2)3
Multiply 2 by 2.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4+(-a2)3
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4+(-a2)3
Apply the product rule to -a2.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4+(-1)3(a2)3
Raise -1 to the power of 3.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4-(a2)3
Multiply the exponents in (a2)3.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4-a2⋅3
Multiply 2 by 3.
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4-a6
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4-a6
a6-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4-a6
Subtract a6 from a6.
-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4+0
Add -3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4 and 0.
-3a4b2+3a2b4-b6+b6-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4
Add -b6 and b6.
-3a4b2+3a2b4+0-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4
Add -3a4b2 and 0.
-3a4b2+3a2b4-3b4c2+3b2c4-c6+c6-3c4a2+3c2a4
Add -c6 and c6.
-3a4b2+3a2b4-3b4c2+3b2c4+0-3c4a2+3c2a4
Add -3a4b2 and 0.
-3a4b2+3a2b4-3b4c2+3b2c4-3c4a2+3c2a4
Factor 3 out of -3a4b2+3a2b4-3b4c2+3b2c4-3c4a2+3c2a4.
Tap for more steps…
Factor 3 out of -3a4b2.
3(-a4b2)+3a2b4-3b4c2+3b2c4-3c4a2+3c2a4
Factor 3 out of 3a2b4.
3(-a4b2)+3(a2b4)-3b4c2+3b2c4-3c4a2+3c2a4
Factor 3 out of -3b4c2.
3(-a4b2)+3(a2b4)+3(-b4c2)+3b2c4-3c4a2+3c2a4
Factor 3 out of 3b2c4.
3(-a4b2)+3(a2b4)+3(-b4c2)+3(b2c4)-3c4a2+3c2a4
Factor 3 out of -3c4a2.
3(-a4b2)+3(a2b4)+3(-b4c2)+3(b2c4)+3(-c4a2)+3c2a4
Factor 3 out of 3c2a4.
3(-a4b2)+3(a2b4)+3(-b4c2)+3(b2c4)+3(-c4a2)+3(c2a4)
Factor 3 out of 3(-a4b2)+3(a2b4).
3(-a4b2+a2b4)+3(-b4c2)+3(b2c4)+3(-c4a2)+3(c2a4)
Factor 3 out of 3(-a4b2+a2b4)+3(-b4c2).
3(-a4b2+a2b4-b4c2)+3(b2c4)+3(-c4a2)+3(c2a4)
Factor 3 out of 3(-a4b2+a2b4-b4c2)+3(b2c4).
3(-a4b2+a2b4-b4c2+b2c4)+3(-c4a2)+3(c2a4)
Factor 3 out of 3(-a4b2+a2b4-b4c2+b2c4)+3(-c4a2).
3(-a4b2+a2b4-b4c2+b2c4-c4a2)+3(c2a4)
Factor 3 out of 3(-a4b2+a2b4-b4c2+b2c4-c4a2)+3(c2a4).
3(-a4b2+a2b4-b4c2+b2c4-c4a2+c2a4)
3(-a4b2+a2b4-b4c2+b2c4-c4a2+c2a4)
Factor (a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3

Solving MATH problems

We can solve all math problems. Get help on the web or with our math app

Scroll to top