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

• The numerical coefficients are 3 and 4. Their GCF is 1.
• The variable $a$ appears as $a^2$ and $a$. The GCF is $a$.
• The variable $b$ appears as $b$ and $b^2$. The GCF is $b$.

The GCF of $3a^2b$ and $4ab^2$ is $1 \cdot a \cdot b = ab$.

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 factor out the greatest common factor (GCF) from both terms.

The coefficients are 7 and 35. The largest number that divides both 7 and 35 is 7.

• For the first term: $7x \div 7 = x$.
• For the second term: $35 \div 7 = 5$.

So, the equivalent expression is $7(x + 5)$.

2.1 What do you notice about all 4 terms?

The given algebraic expression is $xy + 5y + 2x + 10$.
Upon observing all four terms ($xy$, $5y$, $2x$, and 10), we notice that they do not share a common factor (other than 1) across all four terms. This indicates that a technique like factoring by grouping might be used.