Question

How do you multiply `(5n-4)^2`?

Answer 1

`25n^2 - 40 n + 16`

Explanation:

`(a + b)^2 = a^2 + 2ab + b^2`

`(5n + (-4))^2 = (5n)^2 + 2*5n*(-4) + (-4)^2`

Answer 2

`25n^2-40n+16`

Explanation:

`"express " (5n-4)^2=(5n-4)(5n-4)`

`"each term in the second bracket is multiplied by each term"`
`"in the first bracket as shown below"`

`(color(red)(5n-4))(5n-4)`

`=color(red)(5n)(5n-4)color(red)(-4)(5n-4)`

`"distributing gives"`

`=(color(red)(5n)xx5n)+(color(red)(5n)xx-4)+(color(red)(-4)xx5n)+(color(red)(-4)xx-4)`

`=25n^2-20n-20n+16larr" collect like terms"`

`=25n^2-40n+16`