Sure! Let's simplify the expression [tex]\( 6a^2b - 2ba^2 + 3ab - 2ba \)[/tex] step by step by combining like terms.
1. Rewrite the expression:
The given expression is:
[tex]\[
6a^2b - 2ba^2 + 3ab - 2ba
\][/tex]
2. Combine like terms:
Notice that [tex]\(6a^2b\)[/tex] and [tex]\(-2ba^2\)[/tex] are like terms since both contain [tex]\(a^2b\)[/tex]. Similarly, [tex]\(3ab\)[/tex] and [tex]\(-2ba\)[/tex] are like terms since both contain [tex]\(ab\)[/tex].
3. Combine [tex]\(a^2b\)[/tex] terms:
[tex]\[
6a^2b - 2ba^2 = 6a^2b - 2a^2b = (6 - 2)a^2b = 4a^2b
\][/tex]
4. Combine [tex]\(ab\)[/tex] terms:
[tex]\[
3ab - 2ba = 3ab - 2ab = (3 - 2)ab = ab
\][/tex]
So, the expression simplifies to:
[tex]\[
4a^2b + ab
\][/tex]
5. Factor out the common term [tex]\(ab\)[/tex]:
Both terms [tex]\(4a^2b\)[/tex] and [tex]\(ab\)[/tex] contain the common factor [tex]\(ab\)[/tex]. Factoring out [tex]\(ab\)[/tex] gives:
[tex]\[
4a^2b + ab = ab(4a + 1)
\][/tex]
Thus, the simplified form of the expression [tex]\( 6a^2b - 2ba^2 + 3ab - 2ba \)[/tex] is:
[tex]\[
ab(4a + 1)
\][/tex]
This is the final, simplified expression.
