Question

writing an equivalent
apply the distributive property to the expression to write
equivalent expression.
5x + 35
complete the statements.
find the gcf of
now, factor out the gcf by dividing each term in the
expression by
5x divided by the gcf is
, and 35 divided by
the gcf is
the equivalent expression is
.

Explanation:

Step1: Find GCF of 5x and 35

The factors of \(5x\) are \(5\) and \(x\). The factors of \(35\) are \(5\) and \(7\). The greatest common factor (GCF) is \(5\).

Step2: Factor out GCF from \(5x + 35\)

Using the distributive property \(ab+ac=a(b + c)\), factor out \(5\) from each term. Divide \(5x\) by \(5\) to get \(x\), and divide \(35\) by \(5\) to get \(7\). So the equivalent expression is \(5(x + 7)\).

Answer:

• GCF of \(5x\) and \(35\) is \(5\).
• Factor out the GCF (5) by dividing each term in the expression \(5x + 35\) by \(5\).
• \(5x\) divided by \(5\) is \(x\), and \(35\) divided by \(5\) is \(7\).
• The equivalent expression is \(5(x + 7)\).