Page 134 - Start Up Mathematics_8 (Non CCE)

5. The factors of (y – x)a + (x – y)b are:
(a) (x – y)(b – a) (b) (y – x)(b – a) (c) (x – y)(a – b) (d) (y – x)(a + b)

solve Mentally
True or False
1. An algebraic expression is a factor of another algebraic expression if the first can divide the second,
leaving behind a remainder.
2. 1, 9, x, y, xy and 9xy are all the possible factors of 9xy.
2
2
3. 36x – 12xy + y is not a quadratic polynomial.
2
4. On factorizing x + 6x – 27, we get (x – 9)(x + 3).
5. Grouping of terms for the factorization of an algebraic expression is done such that each group has a
common factor.

Fill in the Blanks
1. Factors of a monomial consist of _________, their _________ and the _________ that can divide the
monomial exactly.
5 4
3 3
4 2
2. The HCF of 5x y , 20x y and 25x y is _________.
3. If a given algebraic expression is the _________ of two squares, then it can be factorized by using the
2
2
identity p – q = (p + q)(p – q).
4. The factors of _________ are (a + 2) and (a – 6).
2
5. 2x + 6y – 3(x + 3y) when factorized gives (x + 3y)_________.
Answer in One Word or a Line
1. What do you understand by the term factor of an algebraic expression?
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2
2. Identify the term whose factors are (a – b ) and (a + 1).
4
2
2
2
3. Can 625x – 81 be factorized using the identity p + 2pq + q = (p + q) ?
2
4. What are the factors of x + 2x – 3?
4
2 2
4
5. Which identity will you use to factorize 16p – 56p q + 49q ? What will be its factors?
let’s evaluate
Factorize the following:
4 4
3
2 2
3 5
2 5
(a) 9x y – 27xy (b) 2x y – 3x y + 4x y
2
4
4
(c) y (p + 2q) + y (p + 2q) (d) x – 16
2
2
(e) y + ay + by + ab (f) (x – y) – (x + y) 2
3 2
(g) 16 – 24y + 9y 2 (h) 75x y – 108xy 4
2
(i) y + y + 1 (j) x + 6x – 16
2
4
2
2
2
2
(k) (x + 4x) – 5(x + 4x) – y(x + 4x) + 5y
Thinking Skills
Factorize the following:
2
2
2
(a) x - 25 x 5+ (b) (x + 2)(x + 25) – 10x – 20x
2
4
2
2
(c) y + 5y + 9 (d) (a – 4a)(a – 4a –1) – 20
2 2
8
4 4
4
(e) x – 14x y – 51y 4 (f) x – 11x y – 80y 8
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