Simplify (a+bx^3)^2dx

Math
(a+bx3)2dx
Rewrite (a+bx3)2 as (a+bx3)(a+bx3).
(a+bx3)(a+bx3)dx
Expand (a+bx3)(a+bx3) using the FOIL Method.
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Apply the distributive property.
(a(a+bx3)+bx3(a+bx3))dx
Apply the distributive property.
(a⋅a+a(bx3)+bx3(a+bx3))dx
Apply the distributive property.
(a⋅a+a(bx3)+bx3a+bx3(bx3))dx
(a⋅a+a(bx3)+bx3a+bx3(bx3))dx
Simplify and combine like terms.
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Simplify each term.
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Multiply a by a.
(a2+a(bx3)+bx3a+bx3(bx3))dx
Multiply b by b by adding the exponents.
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Move b.
(a2+abx3+bx3a+b⋅bx3x3)dx
Multiply b by b.
(a2+abx3+bx3a+b2x3x3)dx
(a2+abx3+bx3a+b2x3x3)dx
Multiply x3 by x3 by adding the exponents.
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Move x3.
(a2+abx3+bx3a+b2(x3x3))dx
Use the power rule aman=am+n to combine exponents.
(a2+abx3+bx3a+b2x3+3)dx
Add 3 and 3.
(a2+abx3+bx3a+b2x6)dx
(a2+abx3+bx3a+b2x6)dx
(a2+abx3+bx3a+b2x6)dx
Add abx3 and bx3a.
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Reorder b and a.
(a2+abx3+abx3+b2x6)dx
Add abx3 and abx3.
(a2+2abx3+b2x6)dx
(a2+2abx3+b2x6)dx
(a2+2abx3+b2x6)dx
Apply the distributive property.
(a2d+2abx3d+b2x6d)x
Apply the distributive property.
a2dx+2abx3dx+b2x6dx
Simplify.
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Multiply x3 by x by adding the exponents.
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Move x.
a2dx+2ab(x⋅x3)d+b2x6dx
Multiply x by x3.
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Raise x to the power of 1.
a2dx+2ab(x1x3)d+b2x6dx
Use the power rule aman=am+n to combine exponents.
a2dx+2abx1+3d+b2x6dx
a2dx+2abx1+3d+b2x6dx
Add 1 and 3.
a2dx+2abx4d+b2x6dx
a2dx+2abx4d+b2x6dx
Multiply x6 by x by adding the exponents.
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Move x.
a2dx+2abx4d+b2(x⋅x6)d
Multiply x by x6.
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Raise x to the power of 1.
a2dx+2abx4d+b2(x1x6)d
Use the power rule aman=am+n to combine exponents.
a2dx+2abx4d+b2x1+6d
a2dx+2abx4d+b2x1+6d
Add 1 and 6.
a2dx+2abx4d+b2x7d
a2dx+2abx4d+b2x7d
a2dx+2abx4d+b2x7d
Simplify (a+bx^3)^2dx

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