Just did a specific one of these; let's do the general case.
The point nearest the origin is (a,b).
The line from the origin through the point is
The line we seek is perpendicular to this one. We swap the coefficients on x and y, negating one, to get the perpendicular family of lines. We set the constant by plugging in the point (a,b):
That's standard form; let's plug in the numbers:
The equivalent expressions are 2(24m + 21n) and 3(16m + 14n) and 6(8m + 7n)
<em><u>Solution:</u></em>
Given that, we have to factor the given expression
<em><u>Given expression is:</u></em>
48m + 42n
The equivalent expressions can be found by factoring out the common factors of 48 and 42
<em><u>Let us first find the factors of 48 and 42</u></em>
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
Now factor out 3 from given expression
Now factor out 6 from given expression
Thus the equivalent expressions are 2(24m + 21n) and 3(16m + 14n) and 6(8m + 7n)