# 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?

Jul 18, 2016

$\left(9 \times {t}^{2}\right) + \left({t}^{2} + 2\right)$

OR ${\left(9 \times t\right)}^{2} + \left({t}^{2} + 2\right)$

#### 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.

'The PRODUCT of 9 AND t squared' is not quite clear and could be :
$\left(9 \times {t}^{2}\right) \mathmr{and} {\left(9 \times t\right)}^{2}$

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 $\left({t}^{2} + 2\right)$

So the first expression , $\left(9 \times {t}^{2}\right)$ has the second expression $\left({t}^{2} + 2\right)$ added to it. (increased by).

$\left(9 \times {t}^{2}\right) + \left({t}^{2} + 2\right) \text{ } \left[\mathmr{and} {\left(9 \times t\right)}^{2} + \left({t}^{2} + 2\right)\right]$

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.

Jul 18, 2016

Break up the problem into parts:

#### Explanation:

"t squared" $= {t}^{2}$
"the product of 9 and t squared"$= 9 \times {t}^{2} \mathmr{and} 9 {t}^{2}$.......(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):
$9 {t}^{2} + {t}^{2} + 2 = 10 {t}^{2} + 2$

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:
$81 + 18 t + {t}^{2}$

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.