To find the missing expression in the given equation [tex]\(4 a^2 \times \quad = 4 a^3 b\)[/tex], follow these steps:
1. Identify the given parts of the equation:
[tex]\[
4 a^2 \times \quad = 4 a^3 b
\][/tex]
Here, we need to find the term that, when multiplied by [tex]\(4 a^2\)[/tex], results in [tex]\(4 a^3 b\)[/tex].
2. Set up the equation to solve for the missing term:
Let [tex]\(x\)[/tex] be the missing term. Thus, the equation becomes:
[tex]\[
4 a^2 \times x = 4 a^3 b
\][/tex]
3. Isolate [tex]\(x\)[/tex] on one side of the equation:
To solve for [tex]\(x\)[/tex], divide both sides of the equation by [tex]\(4 a^2\)[/tex]:
[tex]\[
x = \frac{4 a^3 b}{4 a^2}
\][/tex]
4. Simplify the right-hand side:
Simplify the fraction by canceling out the common factors. The [tex]\(4\)[/tex]'s cancel out:
[tex]\[
x = \frac{a^3 b}{a^2}
\][/tex]
5. Simplify further by reducing the [tex]\(a\)[/tex] terms:
Since [tex]\(a^3\)[/tex] divided by [tex]\(a^2\)[/tex] is [tex]\(a\)[/tex]:
[tex]\[
x = a b
\][/tex]
Thus, the missing term [tex]\(x\)[/tex] in the original equation is [tex]\(a b\)[/tex].
Therefore, the complete equation is:
[tex]\[
4 a^2 \times a b = 4 a^3 b
\][/tex]
This confirms that our solution is correct. The term that completes the equation is [tex]\(a b\)[/tex].
