(i) $- z^{2} + 13 z^{2} - 5 z + 7 z^{3} - 15 z$
(ii) p-(p-q)-q-(q-p)
(iii)3a-2b-ab-(a-b+ab)+3ab
(iv) $5 x^{2} y - 5 x^{2} + 3 y x^{2} - 3 y^{2} + x^{2} - y^{2} + 8$

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Solution

$i i) p - (p - q) - q - (q - p)$
$= (p - q) - (p - q) - (q - p)$
$= p - q$

$i i i) 3 a - 2 b - a b - (a - b + a b) + 3 a b$
$= 3 a - 2 b + 2 a b - (a - b + a b)$
$= a + 2 (a - b + a b) - (a - b + a b)$
$= a + a - b + a b$
$= 2 a - b + a b$

$i v) 5 x^{2} y - 5 x^{2} + 3 y x^{2} - 3 y x - 3 y^{2} + x^{2} - y^{2} + 8$
$= 8 x^{2} y - 4 x^{2} - 4 y^{2} + 8$
$= 4 x^{2} (2 y - 1) - 4 (y^{2} - 2)$

$i) - z^{2} + B z^{2} - 5 z + 7 z^{3} - 15 z$
$= 7 z^{3} + 12 z^{2} - 20 z$
$= z (7 z^{2} + 12 z - 20)$

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Similar questions

Simplify combining like terms:

(i) 21b − 32 + 7b − 20b

(ii) − z² + 13z² − 5z + 7z³ − 15z

(iii) p − (p − q) − q − (q − p)

(iv) 3a − 2b − ab − (a − b + ab) + 3ab + b − a

(v) 5x²y − 5x² + 3y x² − 3y² + x²− y²+ 8xy² −3y²

(vi) (3 y²+ 5y − 4) − (8y − y² − 4)

Question 1 (ii)

Simplify combining like terms:

$- z^{2} + 13 z^{2} - 5 z + 7 z^{3} - 15 z$

- z^{2} + 13 z^{2} - 5 z + 7 z^{3} - 15 z

5 x^{2} y - 5 x^{2} + 3 y x^{2} - 3 y^{2} + x^{2} - y^{2} + 8 x y^{2} - 3 y^{2}

5 x^{2} y - 5 x^{2} + 3 y x^{2} - 3 y^{2} + x^{2} - y^{2} + 8 x y^{2} - 3 y^{2}

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