Question

1. (example 3)
2. (2b + 3a)(c²)

Explanation:

Step1: Apply distributive property

We use the distributive property of multiplication over addition, which states that \(a(b + c)=ab+ac\). Here, \(a = c^{2}\), \(b = 2b\), and \(c = 3a\). So we distribute \(c^{2}\) to both terms inside the parentheses.
\((2b + 3a)(c^{2})=2b\times c^{2}+3a\times c^{2}\)

Step2: Simplify the terms

Simplify each product. The product of a variable and a different variable raised to a power is just the product of the coefficients (in this case, the coefficients are 1 for the variables with no written coefficient) and the variables multiplied together. So \(2b\times c^{2}=2bc^{2}\) and \(3a\times c^{2}=3ac^{2}\).
So the simplified form is \(2bc^{2}+3ac^{2}\)

Answer:

\(2bc^{2}+3ac^{2}\)