Respuesta :
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
[tex]48m + 42n = 2(24m+21n)[/tex]
Now factor out 3 from given expression
[tex]48m + 42n = 3(16m + 14n)[/tex]
Now factor out 6 from given expression
[tex]48m+42n=6(8m + 7n)[/tex]
Thus the equivalent expressions are 2(24m + 21n) and 3(16m + 14n) and 6(8m + 7n)
Answer:
Step-by-step 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
