How do you simplify 12a(a^{2}+b)-5b(b^{2}+a)+9b(b^{2}+a)-3a(a^{2}+b)?

ebnspmia0jj

ebnspmia0jj

Answered question

2022-02-05

How do you simplify 12a(a2+b)5b(b2+a)+9b(b2+a)3a(a2+b)?

Answer & Explanation

venenolundicoofw

venenolundicoofw

Beginner2022-02-06Added 12 answers

Step 1
Expand the brackets
12a(a2+b)5b(b2+a)+9b(b2+a)3a(a2+b)=
(12a)(a2)+(12a)(b)(5b)(b2)+(5b)(a)+(9b)(b2)+(9b)(a)(3a)(a2)+(3a)(b)=
which gives us
12a3+12ab5b35ab+9b3+9ab3a33ab
Step 2
Collect like terms
12a35b35ab+9b3+9ab3a33ab=9a35b35ab+9b3+9ab3ab
9a3+12ab5b35ab+9b3+9ab3ab=9a3+13ab5b3+9b3
9a3+13ab5b3+9b3=9a3+13ab+4b3
Answer:
9a3+13ab+4b3
s3au1d8wh

s3au1d8wh

Beginner2022-02-07Added 11 answers

Given: 9a3+13ab+4b3
12a(a2+b)5b(b2+a)+9b(b2+a)3a(a2+b)
Use the distributive property to multiply 12a by a a2+b.
12a3+12ab5b(b2+a)+9b(b2+a)3a(a2+b)
Use the distributive property to multiply 9b by b2+a.
12a3+12ab5b(b2+a)+9b3+9ba3a(a2+b)
Use the distributive property to multiply -5b by b2+a.
12a3+12ab5b35ba+9b3+9ba3a(a2+b).
Combine 12ab and -5ba to get 7ab.
12a3+7ab5b3+9b3+9ba3a(a2+b)
Combine 5b3and 9b3to get 4b3.
12a3+7ab+4b3+9ba3a(a2+b)
Combine 7ab and 9ba to get 16ab.
12a3+16ab+4b33a(a2+b)
Use the distributive property to multiply 3aby a2+b.
12a3+16ab+4b33a33ab
Combine 12a3and 3a3 to get 9a3.
9a3+16ab+4b33ab
Combine 16ab and -3ab to get 13ab.
9a3+13ab+4b3

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