The problem asks us to factorize the given expressions.

1. Problem Description

The problem asks us to factorize the given expressions.

2. Solution Steps

We need to find the greatest common factor (GCF) of the terms in each expression and factor it out.

a) $3y + 15$

The GCF of $3y$ and $15$ is $3$.

Factoring out $3$ gives: $3(y + 5)$

b) $4w - 6$

The GCF of $4w$ and $6$ is $2$.

Factoring out $2$ gives: $2(2w - 3)$

c) $5m + 154$

The GCF of $5m$ and $154$ is $1$.

So the expression is already in its simplest form.

However, if it's $5m + 15$, then the GCF is $5$.

Factoring out $5$ gives: $5(m+3)$

d) $3y + 15$

The GCF of $3y$ and $15$ is $3$.

Factoring out $3$ gives: $3(y + 5)$

e) $4w - 6$

The GCF of $4w$ and $6$ is $2$.

Factoring out $2$ gives: $2(2w - 3)$

f) $5m + 15$

The GCF of $5m$ and $15$ is $5$.

Factoring out $5$ gives: $5(m + 3)$

g) $15y + 20$

The GCF of $15y$ and $20$ is $5$.

Factoring out $5$ gives: $5(3y + 4)$

3. Final Answer

$3(y + 5)$

$2(2w - 3)$

$5(m+3)$ if the expression is $5m+15$, $5m + 154$ can not be simplified.

$3(y + 5)$

$2(2w - 3)$

$5(m + 3)$

$5(3y + 4)$