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(a) Add: p( p - q), q(q - r ) and r (r - p)
(b) Add: 2x (z - x - y) and 2y(z- y - x)
(c) Subtract: 3l (l - 4m + 5n) from 4l (10n - 3m + 2l )
(d) Subtract: 3a(a + b + c) - 2b(a - b + c) from 4c (-a + b + c)

Solution:

We know that addition and subtraction takes place between like terms.

(a) First expression = p ( p - q) = p² - pq

Second expression = q (q - r ) = q² - qr

Third expression = r (r - p) = r ² - pr

Adding these expressions, we get

(a) Add: p( p - q), q(q - r ) and r (r - p) (b) Add: 2x (z - x - y) and 2y(z- y - x) (c) Subtract: 3l (l - 4m + 5n) from 4l (10n - 3m + 2l ) (d) Subtract: 3a(a + b + c) - 2b(a - b + c) from 4c (-a + b + c)

Therefore, the sum of the given expressions is p² + q² + r² - pq - qr - rp.

(b) First expression = 2x ( z - x - y ) = 2xz - 2x² - 2xy

Second expression = 2 y ( z - y - x) = 2 yz - 2 y² - 2 yx

Adding these expressions, we get

(a) Add: p( p - q), q(q - r ) and r (r - p) (b) Add: 2x (z - x - y) and 2y(z- y - x) (c) Subtract: 3l (l - 4m + 5n) from 4l (10n - 3m + 2l ) (d) Subtract: 3a(a + b + c) - 2b(a - b + c) from 4c (-a + b + c)

Therefore, the sum of the given expressions is -2x² - 2 y² - 4xy + 2 yz + 2zx.

(c) First expression = 3l (l - 4m + 5n) = 3l² -12lm + 15ln

Second expression = 4l (10n - 3m + 2l ) = 40ln -12lm + 8l²

Subtracting these expressions, we get

(a) Add: p( p - q), q(q - r ) and r (r - p) (b) Add: 2x (z - x - y) and 2y(z- y - x) (c) Subtract: 3l (l - 4m + 5n) from 4l (10n - 3m + 2l ) (d) Subtract: 3a(a + b + c) - 2b(a - b + c) from 4c (-a + b + c)

Therefore, the result is 5l² + 25ln.

(d) First expression = 3a (a + b + c) - 2b (a - b + c)

= 3a² + 3ab + 3ac - 2ba + 2b² - 2bc

= 3a²+ 2b² + ab + 3ac - 2bc

Second expression = 4c (- a + b + c) = -4ac + 4bc + 4c²

Subtracting these expressions, we obtain

(a) Add: p( p - q), q(q - r ) and r (r - p) (b) Add: 2x (z - x - y) and 2y(z- y - x) (c) Subtract: 3l (l - 4m + 5n) from 4l (10n - 3m + 2l ) (d) Subtract: 3a(a + b + c) - 2b(a - b + c) from 4c (-a + b + c)

Therefore, the result is -3a² - 2b² + 4c² - ab + 6bc - 7ac.

☛ Check: NCERT Solutions Class 8 Maths Chapter 9

Video Solution:

(a) Add: p( p - q), q(q - r ) and r (r - p) (b) Add: 2x (z - x - y) and 2y(z- y - x) (c) Subtract: 3l (l - 4m + 5n) from 4l (10n - 3m + 2l ) (d) Subtract: 3a(a + b + c) - 2b(a - b + c) from 4c (-a + b + c)

NCERT Solutions Class 8 Maths Chapter 9 Exercise 9.3 Question 5

Summary:

The results of the given expressions (a) Add: p( p - q), q(q - r ) and r (r - p) (b) Add: 2x (z - x - y) and 2y(z- y - x) (c) Subtract: 3l (l - 4m + 5n) from 4l (10n - 3m + 2l ) (d) Subtract: 3a(a + b + c) - 2b(a - b + c) from 4c (-a + b + c) are: (a) p² + q² + r² - pq - qr - rp, (b) -2x² - 2 y² - 4xy + 2 yz + 2zx, (c) 5l² + 25ln, (d) -3a² - 2b² + 4c² - ab + 6bc - 7ac

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