Find the best tutors and institutes for Class 8 Tuition
Search in
Carry out the multiplication of the expressions in each of the following pairs.
(i) 4p, q + r (ii) ab, a − b (iii) a + b, 7a2b2
(iv) a2 − 9, 4a (v) pq + qr + rp, 0
(i) (4p) × (q + r) = (4p × q) + (4p × r) = 4pq + 4pr
(ii) (ab) × (a − b) = (ab × a) + [ab × (− b)] = a2b− ab2
(iii) (a + b) × (7a2b2) = (a × 7a2b2) + (b × 7a2b2) = 7a3b2+ 7a2b3
(iv) (a2 − 9) × (4a) = (a2 × 4a) + (− 9) × (4a) = 4a3 − 36a
(v) (pq + qr + rp) × 0 = (pq × 0) + (qr × 0) + (rp × 0) = 0
Find the product.
(i)
(ii) 
(iii) 
(i) (a2) × (2a22) × (4a26) = 2 × 4 ×a2 × a22 × a26 = 8a50
(ii) 
(iii) 
(iv) x × x2 × x3 × x4 = x10
(a) Simplify 3x (4x −5) + 3 and find its values for (i) x = 3, (ii) 
.
(b) a (a2 + a + 1) + 5 and find its values for (i) a = 0, (ii) a = 1, (iii) a = − 1.
(a) 3x (4x − 5) + 3 = 12x2 − 15x + 3
(i) For x = 3, 12x2 − 15x + 3 = 12 (3)2 − 15(3) + 3
= 108 − 45 + 3
= 66
(ii) For
(b)a (a2 + a + 1) + 5 = a3 + a2 + a + 5
(i) For a = 0, a3 + a2 + a + 5 = 0 + 0 + 0 + 5 = 5
(ii) For a = 1, a3 + a2 + a + 5 = (1)3 + (1)2 + 1 + 5
= 1 + 1 + 1 + 5 = 8
(iii) For a = −1, a3 + a2 + a + 5 = (−1)3 + (−1)2 + (−1) + 5
= − 1 + 1 − 1 + 5 = 4
(a) Add:
(b) Add: and
(c) Subtract: and
(d) Subtract: 3a(a+b+c)-2b(a-b+c) from 4c(-a+b+c)
(a) First expression = p (p − q) = p2 − pq
Second expression = q (q − r) = q2 − qr
Third expression = r (r − p) = r2 − pr
Adding the three expressions, we obtain
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 = 2y (z − y − x) = 2yz − 2y2 − 2yx
Adding the two expressions, we obtain
Therefore, the sum of the given expressions is − 2x2 − 2y2 − 4xy + 2yz + 2zx.
(c) 3l (l − 4m + 5n) = 3l2 − 12lm + 15ln
4l (10n − 3m + 2l) = 40ln − 12lm + 8l2
Subtracting these expressions, we obtain
Therefore, the result is 5l2 + 25ln.
(d) 3a (a + b + c) − 2b (a − b + c) = 3a2 +3ab + 3ac − 2ba + 2b2 − 2bc
= 3a2 + 2b2 + ab + 3ac − 2bc
4c (− a + b + c) = − 4ac + 4bc + 4c2
Subtracting these expressions, we obtain
Therefore, the result is −3a2 −2b2 + 4c2− ab + 6bc − 7ac.
How helpful was it?
How can we Improve it?
Please tell us how it changed your life *
Please enter your feedback
UrbanPro.com helps you to connect with the best Class 8 Tuition in India. Post Your Requirement today and get connected.
Find best tutors for Class 8 Tuition Classes by posting a requirement.
Get started now, by booking a Free Demo Class
