(a) Add $p (p - q), q (q - r)$ and $r (r - p)$

(b) Add $2 x (z - x - y)$ and $27 (z - y - x)$
(c) Subtract $3 l (l - 4 m + 5 n)$ from $4 l (10 n - 3 m + 2 l)$
(d) Subtract $3 a (a + b + c) - 2 b (a - b + c)$ from $4 c (- a + b + c)$

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Solution

a) $p (p - q) + q (q - r) + r (r - p) = p^{2} - p q + q^{2} - q r + r^{2} - p r$

$= p^{2} + q^{2} + r^{2} - p q - q r - r p$

b) $2 x (z - x - y) + 27 (z - y - x) = 2 x z - 2 x^{2} - 2 x y + 27 z - 27 y - 27 z$

c) $4 l (10 n - 3 m + 2 l) - 3 l (l - 4 m + 5 n) = 40 l n - 12 l m + 8 l^{2} - 3 l^{2} + 12 l m - 15 l n$

$= 25 l n + 5 l^{2}$

d) $4 c (- a + b + c) - [3 a (a + b + c) - 2 b (a - b + c)] = - 4 a c + 4 b c + 4 c^{2} - [3 a^{2} + 3 a b + 3 a c - 2 a b + 2 b^{2} - 2 b c]$

$= - 4 a c + 4 b c + 4 c^{2} - 3 a^{2} - a b - 3 a c - 2 b^{2} + 2 b c$

Suggest Corrections

Similar questions

(a)Add: $p (p - q), q (q - r)$ and $r (r - p)$

(b)Add: $2 x (z - x - y)$ and $2 y (z - y - x)$

(c)Subtract: $3 l (l - 4 m + 5 n)$ from $4 l (10 n - 3 m + 2 l)$

(d)Subtract: $3 a (a + b + c) - 2 b (a - b + c)$ from $4 c (- a + b + c)$

3 l (l - 4 m + 5 n)

4 l (10 n - 3 m + 2 l)

3 a (a + b + c) - 2 b (a - b + c)

4 c (- a + b + c)

3 l (l - 4 m + 5 n) f r o m 4 l (10 n - 3 m + 2 l) .

Question 81 (vi)

Add:

3a(a - b + c) , 2b(a - b + c)