Page 112 - Start Up Mathematics_8 (Non CCE)

Fill in the Blanks
1. In algebraic expressions, the elements separated by + or – sign are called ___________.
2. Algebraic expressions with ___________ terms are called trinomials.
3. Terms with identical symbolic variables are called _________ terms and the others are called ________ terms.
2
2
4. 2x – 3y, 6xy + 7 and 3a b + 5ab are examples of ____________.
5. Multiplication of two ___________ involves repeated use of law of commutativity and the law of
___________ of multiplication.

Answer in One Word or a Line
1. What is an algebraic expression? Give an example.
2. What are factors of an algebraic expression?
3. Define algebraic identity.
4. How can you distinguish between an identity and an equation?
5. Which property is utilized in multiplication of two binomials?
6. State the standard identities.

let’s evaluate
3 2 2 2 4 2 2 2 2
2
1. Add: (a) ab – a b, ab + ab (b) 4x + 3x – 7, 2x – 5x + 6, x + 2x + 4
2
4 3 5 5
2. Subtract:
7 5 4 3 2x 3 5 x 11 2 5 2 3 7 5
2
2
(a) x - x + + x from - x + - (b) xz - xy + yz from xy - xz - yz
3
6 6 7 7 7 7 6 6 3 7 3 2 4 6
Ê 1 4 ˆ Ê 1 2 ˆ Ê 2 2 ˆ
2
2
32x ˜ - Á
3. Simplify Á x - x + 11 ˜ – Á x -+ x - x + 2 ˜
Ë 3 7 ¯ Ë 7 ¯ Ë 7 3 ¯
2 ˆ
2 2 2
3
10 30 20
2 3 2
2
4. Calculate: (a) (15x y z ) ¥ (20x y z ) (b) Ê 2 xy z ¥ (1.5xyz ) ¥ (1.15x y z ) ¥ (3xyz)
Á
˜
Ë
¯
3
5. Find the following products:
-8 Ê 3 9 2 3 ˆ 2 2
2
(a) abc Á abc - ab c ˜ (b) (4x – 3y )(2x + 5y)
27 Ë 2 4 ¯
2
(c) (4x – 5x + 8) ¥ (8x + 3) (d) Ê Á Ë 3 xy + 2 ˆ Ê 9 x yz - 3 xyz 2 ˆ ˜ ¯
x ¥
2
2
˜ Á
5 ¯ Ë
5
2
4
Ê 4 2 ˆ Ê 4 2 ˆ
y
y
(e) (4x – 9) ¥ (4x + 5) (f) Á 3 x - 3 ¯ Ë 3 x + 3 ¯ ˜
˜ Á
Ë
6. Simplify the following:
2
2
2
2
(a) 4lm(l – m) – 6l (m – m ) – 3m (2l – l) + 2lm(l – m)
2
(b) (3x + 2y)(3x + 2y) – (4x – 3y) + (2x + 3y)(2x – 3y)
2
(c) (3l + 4m) – (3l + 4m)(3l – 4m) – (5l – 7m) 2
2
2
2
7. If x + y + z – xy – yz – zx = 0, prove that x = y = z.
8. Evaluate the following using a suitable identity:
2
2
2
2
(a) (99) (b) (106) (c) 47 ¥ 53 (d) 122 – 22 (e) 36 ¥ 34
9. Find the product:
4
2
4
2
(a) (2y – 1)(2y + 1)(4y + 1)(16y + 1) (b) (x – 2)(x + 2)(x + 4)(x + 16)
1 2 1 1
10. If x + = 9 and x + = 53, find x – .
x x 2 x
104