Add
$t - t^{2} - 14$ , $15 t^{3} + 13 + 9 t - 8 t^{2}$ , $12 t^{2} - 19 - 24 t$ and $4 t - 9 t^{2} + 19 t^{3}$ .

If $t = - 1$ find the value of the expression. [4 MARKS]

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Solution

Forming equation: 1 Mark
Steps: 1 Mark
Answer: 1 Mark
Value: 1 Mark

Here while adding the algebraic expressions we need to know that we can only add the like terms.
Like terms are those terms which have the same algebraic factors.

Sum

$= (t - t^{2} - 14) + (15 t^{3} + 13 + 9 t - 8 t^{2}) + (12 t^{2} - 19 - 24 t) + (4 t - 9 t^{2} + 19 t^{3})$
$= t - t^{2} - 14 + 15 t^{3} + 13 + 9 t - 8 t^{2} + 12 t^{2} - 19 - 24 t + 4 t - 9 t^{2} + 19 t^{3}$
$= (t + 9 t - 24 t + 4 t) + (- t^{2} - 8 t^{2} + 12 t^{2} - 9 t^{2}) + (- 14 + 13 - 19) + (15 t^{3} + 19 t^{3})$
$= - 10 t - 6 t^{2} - 20 + 34 t^{3}$

Hence, the required expression is $- 10 t - 6 t^{2} - 20 + 34 t^{3}$ .

Given that:
$t = - 1$
On substituting the values we get:
$- 10 t - 6 t^{2} - 20 + 34 t^{3}$
$= - 10 \times (- 1) - 6 \times (- 1)^{2} - 20 + 34 \times (- 1)^{3}$
$= 10 - 6 - 20 - 34$
$= - 50$

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