Question

How do you find the product `(3/4k+8)^2`?

Answer 1

`(3/4k + 8)^2 = 9/36k^2 + 12k + 64`

Explanation:

`(x+y)^2 = x^2 + 2xy + y^2`

Answer 2

`(9k^2)/16 +12k +64`

Explanation:

The mistake most people make is simply squaring both terms individually, so you to avoid this error, you should start by writing out the binomial like this:
`(3/4k +8)(3/4k+8)`

This is because it was squared; if it was cubed, you'd write it thrice, and so on.

This makes it easier to visualise what exactly you're doing, therefore you're less likely to make mistakes when solving it.

Now, I don't know if you've heard of FOIL method but I'll link a video here so you can understand it better before continuing with the question: enter link description here

So, using the FOIL method, we need to multiply:
the first terms of each binomial. i.e. `3/4k * 3/4k` which is `(9k^2)/16`
Then the outer terms, i.e. `3/4k*8` which gives `(24k)/4`
Then the inside terms, i.e `8*3/4k` which is `(24k)/4`
And finally the last terms, i,e, `8*8` which is `64`

Now you'll need to add these terms:
`(9k^2)/16 + (24k)/4 +(24k)/4+64`

[you can add the terms with the same variable; but remember: you can't add `k^2` and `k` because they have different powers.]

So,
`(9k^2)/16+ (48k)/4+64`

You can also now simplify the individual fractions, which is:
`(9k^2)/16 +12k +64`