Form the sum of $(4 + 3 x - x^{2})$ and $(5 - 4 x + 2 x^{2})$ , subtract the sum of $(3 x^{2} - 5 x)$ and $(- x^{2} + 2 x + 5)$ .

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Solution

$(4 + 3 x - x^{2}) + (5 - 4 x + 2 x^{2}) - [(- 5 x + 3 x^{2}) + (5 + 2 x - x^{2})]$
$= (4 + 5 + 3 x - 4 x - x^{2} + 2 x^{2}) - [5 - 5 x + 2 x + 3 x^{2} - x^{2}]$
$= (9 - x + x^{2}) - (5 - 3 x + 2 x^{2})$
$= 9 - 5 - x + 3 x + x^{2} - 2 x^{2}$
$= 4 + 2 x - x^{2}$
$∴ (- x^{2} + 2 x + 4)$

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Question 6 (b)

From the sum of $4 + 3 x a n d 5 - 4 x + 2 x^{2}$ , subtract the sum of $3 x^{2} - 5 x a n d - x^{2} + 2 x + 5$ .

4 + 3 x

5 - 4 x + 2 x^{2}

3 x^{2} - 5 x

- x^{2} + 2 x + 5

4 + 3 x a n d 5 - 4 x + 2 x^{2}

3 x^{2} - 5 x a n d - x^{2} + 2 x + 5

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