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Factor 48m + 42n to identify the equivalent expressions

2 Answers

2 votes

Answer:

Explanation:

To factor means to rewrite an expression as a product. Let's try dividing the expression 48m+42n48m+42n48, m, plus, 42, n by each factor.

Hint #22 / 6

Factoring out 666

\begin{aligned} &\phantom{=}48m+42n\\\\ &=6\left(\dfrac{48m+42n}{6}\right)\\\\ &=6\left(\dfrac{48m}{6}+\dfrac{42n}{6}\right) \\\\ &=6(8m+7n) \end{aligned}

=48m+42n

=6(

6

48m+42n

)

=6(

6

48m

+

6

42n

)

=6(8m+7n)

Yes, 48m+42n48m+42n48, m, plus, 42, n is equivalent to 6(8m+7n)6(8m+7n)6, left parenthesis, 8, m, plus, 7, n, right parenthesis.

Hint #33 / 6

Factoring out 333

\begin{aligned} &\phantom{=}48m+42n\\\\ &=3\left(\dfrac{48m+42n}{3}\right)\\\\ &=3\left(\dfrac{48m}{3}+\dfrac{42n}{3}\right) \\\\ &=3(16m+14n) \end{aligned}

=48m+42n

=3(

3

48m+42n

)

=3(

3

48m

+

3

42n

)

=3(16m+14n)

Yes, 48m+42n48m+42n48, m, plus, 42, n is equivalent to 3(16m+14n)3(16m+14n)3, left parenthesis, 16, m, plus, 14, n, right parenthesis.

Hint #44 / 6

Factoring out 222

\begin{aligned} &\phantom{=}48m+42n\\\\ &=2\left(\dfrac{48m+42n}{2}\right)\\\\ &=2\left(\dfrac{48m}{2}+\dfrac{42n}{2}\right) \\\\ &=2(24m+21n) \end{aligned}

=48m+42n

=2(

2

48m+42n

)

=2(

2

48m

+

2

42n

)

=2(24m+21n)

No, 48m+42n48m+42n48, m, plus, 42, n is not equivalent to 2(12m+21n)2(12m+21n)2, left parenthesis, 12, m, plus, 21, n, right parenthesis.

Hint #55 / 6

Factoring out 777

\begin{aligned} &\phantom{=}48m+42n\\\\ &=7\left(\dfrac{48m+42n}{7}\right)\\\\ &=7\left(\dfrac{48m}{7}+\dfrac{42n}{7}\right) \\\\ &=7\left(\dfrac{48}{7}m+6n\right) \end{aligned}

=48m+42n

=7(

7

48m+42n

)

=7(

7

48m

+

7

42n

)

=7(

7

48

m+6n)

No, 48m+42n48m+42n48, m, plus, 42, n is not equivalent to 7(7m+6n)7(7m+6n)7, left parenthesis, 7, m, plus, 6, n, right parenthesis.

Hint #66 / 6

The following expressions are equivalent to 48m+42n48m+42n48, m, plus, 42, n:

6(8m+7n)6(8m+7n)6, left parenthesis, 8, m, plus, 7, n, right parenthesis

3(16m+14n)3(16m+14n)3, left parenthesis, 16, m, plus, 14, n, right parenthesis

Related content

User Pkerckhove
by
8.0k points
4 votes

The equivalent expressions are 2(24m + 21n) and 3(16m + 14n) and 6(8m + 7n)

Solution:

Given that, we have to factor the given expression

Given expression is:

48m + 42n

The equivalent expressions can be found by factoring out the common factors of 48 and 42

Let us first find the factors of 48 and 42

The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Thus the common factors are: 1, 2, 3, 6

Let us factor out 2 from given expression


48m + 42n = 2(24m+21n)

Now factor out 3 from given expression


48m + 42n = 3(16m + 14n)

Now factor out 6 from given expression


48m+42n=6(8m + 7n)

Thus the equivalent expressions are 2(24m + 21n) and 3(16m + 14n) and 6(8m + 7n)

User Tucker
by
8.8k points