To expand the binomial expression [tex]\((2x^3 + 3y^2)^7\)[/tex] using the binomial theorem, we need to identify the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] in the binomial [tex]\((a + b)^7\)[/tex].
Let's look at the expression [tex]\((2x^3 + 3y^2)\)[/tex]. Comparing it to the typical binomial form [tex]\((a + b)\)[/tex], we can see that:
- The first term [tex]\(2x^3\)[/tex] corresponds to [tex]\(a\)[/tex].
- The second term [tex]\(3y^2\)[/tex] corresponds to [tex]\(b\)[/tex].
Thus:
- The value of [tex]\(a\)[/tex] should be [tex]\(2x^3\)[/tex].
- The value of [tex]\(b\)[/tex] should be [tex]\(3y^2\)[/tex].
Hence, the correct substitution for the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] is:
[tex]\[ a = 2x^3 \][/tex]
[tex]\[ b = 3y^2 \][/tex]
So, the correct answer is:
[tex]\[ a = 2x^3 \quad \text{and} \quad b = 3y^2 \][/tex]
