Write the expression 3a2b + 4ab2 as an equivalent algebraic expression.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the remaining questions:

1.3 Write the expression $3a^2b + 4ab^2$ as an equivalent algebraic expression.

Identify the Highest Common Factor (H.C.F.) of $3a^2b$ and $4ab^2$ .
From the previous question (1.2), the H.C.F. is $ab$ .
Factor out the H.C.F.
from each term.
$3a^2b + 4ab^2 = ab(3a) + ab(4b)$
Write the expression with the H.C.F.
factored out.
$ab(3a + 4b)$
The equivalent algebraic expression is $\boxed{ab(3a + 4b)}$ .

1.3 Lucy is given the expression below: $7x + 35$ . Explain to Lucy how to find the equivalent expression.

To find an equivalent expression for $7x + 35$ , Lucy needs to factorize it by following these steps:
- Step 1: Find the greatest common factor (GCF) of all terms in the expression. For $7x$ and 35, the GCF is 7.
- Step 2: Divide each term in the original expression by the GCF. This gives $7x \div 7 = x$ and $35 \div 7 = 5$ .
- Step 3: Write the GCF outside a set of parentheses, and place the results from Step 2 inside the parentheses, connected by the original operation. So, $7x + 35$ becomes $7(x + 5)$ .

Answer