Chapter 6: Algebraic Expressions and Identities Exercise – 6.4

Question: 1

Find the products

2a³(3a + 5b)

Solution:

To find the product, we will use distributive law as follows:

Question: 2

Find the products

-11a (3a + 2b)

Solution:

To find the product, we will use distributive law as follows:.

Question: 3

Find the products

- 5a(7a – 2b)

Solution:

To find the product, we will use distributive law as follows:

Question: 4

Find the products

-11y²(3y + 7)

Solution:

To find the product, we will use distributive law as follows:

Question: 5

Find the products

Solution:

To find the product, we will use distributive law as follows:

Question: 6

Find the products

xy (x³- y³)

Solution:

To find the product, we will use distributive law as follows:

Question: 7

Find the products

0.1y (0.1 x⁵ + 0.1y)

Solution:

To find the product, we will use distributive law as follows:

Question: 8

Find the products

Solution:

To find the product, we will use distributive law as follows:

Question: 9

Find the products

Solution:

To find the product, we will use distributive law as follows:

Question: 10

Find the products

Solution:

To find the product, we will use distributive law as follows:

Question: 11

Find the products

1.5 x(10x²y – 100xy²)

Solution:

To find the product, we will use distributive law as follows:

Question: 12

Find the products

4.1 xy(1.1x – y)

Solution:

To find the product, we will use distributive law as follows:

Question: 13

Find the products

Solution:

To find the product, we will use distributive law as follows:

Question: 14

Find the products

Solution:

To find the product, we will use distributive law as follows:

Question: 15

Find the products

Solution:

To find the product, we will use distributive law as follows:

Question: 16

Find the product 24x²(1-2x) and evaluate its value for x = 3.

Solution:

To find the product, we will use distributive law as follows:

Question: 17

Find the product -3y(xy + y²) and find its value for x = 4 and y = 5.

Solution:

To find the product, we will use distributive law as follows:

Question: 18

Multiply – (3/2)x²y³ by (2x – y) and verify the answer for x = 1 and y = 2.

Solution:

To find the product, we will use distributive law as follows:

Question: 19

Multiply the monomial by the binomial and find the value of each for x = -1, y = 0.25 and z = 0.05:

(i) 15y² (2 – 3x)

(ii) −3x (y² + z²)

(iii) Z²(x – y)

(iv) xz(x² + y²)

Solution:

Question: 20

Simplify:

(i) 2x²(x³ – x) –3x(x⁴+ 2x) -2(x⁴-3x²)

(ii) x³y (x² – 2x) + 2xy(x³– x⁴)

(iii) 3a² + 2(a + 2) -3a(2a + 1)

(iv) x(x + 4) + 3x(2x²–1) + 4x² + 4

(v) a(b – c) – b(c – a) – c(a – b)

(vi) a(b – c) + b(c – a) + c(a – b)

(vii) 4ab(a–b) – 6a²(b – b²) –3b²(2a² – a) + 2ab(b – a)

(viii) x²(x² + 1) –x³(x + 1) –x(x³– x)

(ix) 2a²+ 3a(1- 2a³) + a(a + 1)

(x) a²(2a – 1) + 3a + a³ – 8

(xii) a²b(a – b²) + ab²(4ab – 2a²) – a³b(1 – 2b)

(xiii) a²b(a³ – a + 1) – ab(a⁴ –2a² + 2a) – b(a³ – a² – 1)

Solution: