What do you notice about all 4 terms?

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the questions:

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

Find the greatest common factor (GCF) of the terms $3a^2b$ and $4ab^2$ .
The common factors are $a$ and $b$ . The lowest power of $a$ is $a^1$ and the lowest power of $b$ is $b^1$ .
So, the GCF is $ab$ .
Factor out the GCF from each term.
$3a^2b + 4ab^2 = ab(3a) + ab(4b)$ $= \boxed{ab(3a + 4b)}$
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 finding the greatest common factor (GCF).
Identify the terms in the expression, which are $7x$ and 35.
Find the greatest common factor (GCF) of these terms.
The factors of $7x$ are $1, 7, x, 7x$. The factors of 35 are $1, 5, 7, 35$. The GCF is 7.
Divide each term in the expression by the GCF.
$7x \div 7 = x$ $35 \div 7 = 5$
Write the GCF outside a set of parentheses, and the results from Step 3 inside the parentheses, connected by the original operation.
$7(x + 5)$
So, the equivalent expression is $\boxed{7(x + 5)}$ .

ACTIVITY 2
The following algebraic expression is given: $xy + 5y + 2x + 10$

2.1 What do you notice about all 4 terms?

The four terms ( $xy$ , $5y$ , $2x$ , 10) are not like terms, meaning they cannot be combined. There is no single common factor (either a variable or a number) that is present in all four terms.

Step-by-step solution