Question

How do you find the product `(2/5y-4)^2`?

Answer 1

`(2/5y-4)=color(magenta)(4/25y^2-8/5y+16)`

Explanation:

Use the general relation `(a-b)^2=a^2-2ab+b^2`
with `a=2/5y` and `b=4`

or work it through in detail using the distributive property:
`(2/5y-4)^2`
`color(white)("XXX")=color(red)(""(2/5y-4))xxcolor(blue)(""(2/5y-4))`

`color(white)("XXX")=color(red)(2/5y)xxcolor(blue)(""(2/5y-4))color(red)(-4)xxcolor(blue)(""(2/5y-4))`

`color(white)("XXX")=(color(red)(2/5y)xxcolor(blue)(2/5y)-color(red)(2/5y)xxcolor(blue)4)-(color(red)4xxcolor(blue)(2/5y)-color(red)4xxcolor(blue)(""(-4)))`

`color(white)("XXX")=(4/25y^2-8/5y)-(8/5y-16)`

`color(white)("XXX")=4/25y^2-16/5y+16`