Question

Factor 48m + 42n to identify the equivalent expressions

Answer 1

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)