from a handpicked tutor in LIVE 1-to-1 classes

# (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) = p^{2} - pq

Second expression = q (q - r ) = q^{2} - qr

Third expression = r (r - p) = r ^{2} - pr

Adding these expressions, we get

Therefore, the sum of the given expressions is p^{2} + q^{2} + r^{2} - pq - qr - rp.

(b) First expression = 2x ( z - x - y ) = 2xz - 2x^{2} - 2xy

Second expression = 2 y ( z - y - x) = 2 yz - 2 y^{2} - 2 yx

Adding these expressions, we get

Therefore, the sum of the given expressions is -2x^{2} - 2 y^{2} - 4xy + 2 yz + 2zx.

(c) First expression = 3l (l - 4m + 5n) = 3l^{2} -12lm + 15ln

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

Subtracting these expressions, we get

Therefore, the result is 5l^{2} + 25ln.

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

= 3a^{2} + 3ab + 3ac - 2ba + 2b^{2} - 2bc

= 3a^{2 }+ 2b^{2} + ab + 3ac - 2bc

Second expression = 4c (- a + b + c) = -4ac + 4bc + 4c^{2}

Subtracting these expressions, we obtain

Therefore, the result is -3a^{2} - 2b^{2} + 4c^{2} - 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) p^{2} + q^{2} + r^{2} - pq - qr - rp, (b) -2x^{2} - 2 y^{2} - 4xy + 2 yz + 2zx, (c) 5l^{2} + 25ln, (d) -3a^{2} - 2b^{2} + 4c^{2} - ab + 6bc - 7ac

**☛ Related Questions:**

- Carry out the multiplication of the expressions in each of the following pairs. (i) 4 p, q + r (ii) ab, a - b (iii) a + b, 7a2b2 (iv) a2 - 9, 4a (v) pq + qr + rp, 0
- Complete the table.
- Find the product. (i) (a2 ) × (2a22 ) × (4a26) (ii) (2/3 xy) × (-9/10 x2 y2) (iii) (-10/3 pq3 ) × (6/5 p3q) (iv) x × x2 × x3 × x4
- (a) Simplify 3x(4x - 5) + 3 and find its values for (i) x = 3 (ii) x = 1/2 (b) Simplify a (a2 + a + 1)+ 5 and find its values for (i) a = 0, (ii) a =1, (iii) a = - 1

visual curriculum