Certainly! Let's expand the given expression [tex]\(3 x^2(3 x + 2 y)\)[/tex] step-by-step.
The expression is:
[tex]\[ 3 x^2 (3 x + 2 y) \][/tex]
We will use the distributive property (also known as the distributive law of multiplication over addition) to expand the expression. According to this property, [tex]\( a(b + c) = ab + ac \)[/tex].
Here, [tex]\( a = 3 x^2 \)[/tex], [tex]\( b = 3 x \)[/tex], and [tex]\( c = 2 y \)[/tex].
Let's distribute [tex]\(3 x^2 \)[/tex] to both terms inside the parentheses:
1. First, we multiply [tex]\( 3 x^2 \)[/tex] by [tex]\( 3 x \)[/tex]:
[tex]\[ 3 x^2 \cdot 3 x = (3 \cdot 3) x^2 \cdot x = 9 x^3 \][/tex]
2. Next, we multiply [tex]\( 3 x^2 \)[/tex] by [tex]\( 2 y \)[/tex]:
[tex]\[ 3 x^2 \cdot 2 y = (3 \cdot 2) x^2 \cdot y = 6 x^2 y \][/tex]
Now, we combine the two results:
[tex]\[ 9 x^3 + 6 x^2 y \][/tex]
So, the expanded form of the expression [tex]\(3 x^2(3 x + 2 y)\)[/tex] is:
[tex]\[ \boxed{9 x^3 + 6 x^2 y} \][/tex]
