Question

How do you write an algebraic expression of product of 9 and t squared, increased by the sum of the square of t and 2?

Answer 1

`(9 xx t^2) + (t^2 + 2)`

OR `(9 xx t)^2 + (t^2 + 2)`

Explanation:

The product of 9 and t squared, increased by the sum of the square of t and 2.

The words 'product' and 'sum' are always used with the word 'AND" indicating which two values are multiplied or added.

'Increased by' means add.

'The PRODUCT of 9 AND t squared' is not quite clear and could be :
`(9 xx t^2) or (9 xx t)^2`

Although the latter should be written as 'The product of 9 and t, all squared.'

'the SUM of the square of t AND 2' is `(t^2 + 2)`

So the first expression , `(9 xx t^2)` has the second expression `(t^2 + 2)` added to it. (increased by).

`(9 xx t^2) + (t^2 + 2) " "[ or (9 xx t)^2 + (t^2 + 2)]`

The brackets are not necessary but I have left them in for clarity.

This highlights the need for clear precise English with the correct use of Grammar to avoid any misunderstanding.

Answer 2

Break up the problem into parts:

Explanation:

"t squared" `=t^2`
"the product of 9 and t squared"`=9xxt^2or 9t^2`.......(A)

"square of t" `=t^2` (as before)
"sum of square of t and 2"`=t^2+2`......(B)

Then we only have to increase (=add) (A) by (B):
`9t^2+t^2+2=10t^2+2`

Note:
If the original question had been "the sum of squares" (plural!), then answer (B) would have been `t^2+2^2=t^2+4`

If the question meant (9 plus t) squared, answer (A) would be:
`81+18t+t^2`

In short, if I were the maths teacher , I wouldn't be happy with the way I worded this problem -- there are a few ambuigities.