Page 40 - Concepts of Reasoning-8

CHAPTER

Worksheet-6.1 Algebraic Expressions 6

Multiplication of Algebraic Expressions

1. Choose the correct answers from the boxes given below and fill in the blanks :

2
10 11
2 3
3 2
2
2 2
27x y – 15x y – 12x – 12xy 2 60x y – 24x y + 36xy 4 120x y
2
6 9
4 2
a. 8x y × 15x y = ________ b. –12x × (x+y ) = ________
2
2
2
2
c. (9 – 5y) × 3x y = ________ d. (5x – 2xy + 3y ) × 12xy = ________
2. Write the steps of multiplying two algebraic expressions in the correct sequence :
3
a. (3x + 6y) × (7x –4y) Solution :
3
3
= 3x × 7x – 3x × 4y + 6y × 7x – 6y × 4y
3
4
= 21x – 12x y + 42yx – 24y 2
3
= 3x (7x – 4y) + 6y (7x – 4y)
2
2
b. (–2r + 3k) × (2k – 5r)
2
2
2
2
= –2r × 2k – 2r × (– 5r) + 3k × 2k + 3k × (– 5r) Solution :
2
2
2
= –2r ( 2k – 5r) + 3k (2k – 5r)
3
3
2 2
= –4r k + 10r + 6k – 15kr
c. p + 4 1 p
–
2 2 3
p p 2 4p
= – + 2 – Solution :
4 6 3
p 1 p p 1 p
= × – × + 4 × – 4 ×
2 2 2 3 2 3
p 1 p 1 p
= × – + 4 × –
2 2 3 2 3
3. Match the following :
8
3
3
5
4
2
a. 5x p × 2xp i. –2x + 4x – 8x – 16x 2
4
5
3
7
6
2
3
b. –6x (2 + 9p ) ii. 2x + 8x – 2x + 22x – 12x – 42
3 7
7

c. 1 x – 1 x + 1 x +1 × –16x 2 iii. –12x – 54p x
6
3
8 4 2
3
d. (9x – 4p) × (–2x + 6p) iv. 10x p 7
40 Reasoning - 8