Question

How do you completely factor `64m ^ { 2} - 100n ^ { 2} |`?

Answer 1

See a solution process below:

Explanation:

We can use this rule to factor the expression: `64m^2 - 100n^2`

`color(red)(x)^2 - color(blue)(y)^2 = (color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y))`

If we let `color(red)(x)^2 = 64m^2` Then `color(red)(x) = 8m`

If we let `color(blue)(y)^2 = 100n^2` Then `color(blue)(y) = 10n`

Substituting these values into the formula gives:

`color(red)(64m)^2 - color(blue)(100n)^2 = (color(red)(8m) + color(blue)(10n))(color(red)(8m) - color(blue)(10n))`

Answer 2

`4(4m-5n)(4m+5n)`

Explanation:

`"take out a "color(blue)"common factor of 4"`

`rArr4(16m^2-25n^2)to(color(red)(A))`

`16m^2-25n^2" is a "color(blue)"difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`(4m)^2=16m^2rArra=4m`

`(5n)^2=25n^2rArrb=5n`

`rArr16m^2-25n^2=(4m-5n)(4m+5n)`

`"returning to complete "(color(red)(A))`

`=4(4m-5n)(4m+5n)`