Скачать или смотреть ex 14.1 q2 Class 8 Factorisation - Maths Class 8th - chapter 14 Factorise the following expressions

factorize the following expressions:
ex 14.1 q2 Class 8 Factorisation - Maths Class 8th - chapter 14
Factorization is the process of reducing the bracket of a quadratic equation, instead of expanding the bracket and converting the equation to a product of factors which cannot be reduced further. For example, factorising (x²+5x+6) to (x+2) (x+3). Here, (x+2) (x+3) is factorization of a polynomial (x²+5x+6). These factors can be either variable, integers or algebraic expressions. Basically, Factorization is the reverse function of multiplication. A form of disintegration, factorisation entails the gradual breakdown of a polynomial into its factors.
Factors of natural numbers
Factors of algebraic expressions
What is Factorisation?
Method of common factors
Factorization by regrouping terms
What is regrouping?

EXERCISE 14.1
1. Find the common factors of the given terms.
(i) 12x, 36 (ii) 2y, 22xy (iii) 14 pq, 28p2 q2 (iv) 2x, 3x2 , 4 (v) 6 abc, 24ab2 , 12 a2 b (vi) 16 x3 , – 4x2 , 32x (vii) 10 pq, 20qr, 30rp (viii) 3x2 y3 , 10x3 y2 ,6 x2 y2 z
2. Factorize the following expressions.
(i) 7x – 42 (ii) 6p – 12q (iii) 7a2 + 14a (iv) – 16 z + 20 z3 (v) 20 l2 m + 30 a l m (vi) 5 x2 y – 15 xy2 (vii) 10 a2 – 15 b2 + 20 c2 (viii) – 4 a2 + 4 ab – 4 ca (ix) x2 y z + x y2 z + x y z2 (x) a x2 y + b x y2 + c x y z
3. Factorise. (i) x2 + x y + 8x + 8y (ii) 15 xy – 6x + 5y – 2 (iii) ax + bx – ay – by (iv) 15 pq + 15 + 9q + 25p (v) z – 7 + 7 x y – x y z

Factorisation using identities
Factors of the form ( x + a) ( x + b)
EXERCISE 14.2
1. Factorize the following expressions.
(i) a2 + 8a + 16 (ii) p2 – 10 p + 25 (iii) 25m2 + 30m + 9 (iv) 49y2 + 84yz + 36z2 (v) 4x2 – 8x + 4 (vi) 121b2 – 88bc + 16c2 (vii) (l + m)2 – 4lm (Hint: Expand ( l + m)2 first) (viii) a4 + 2a2 b2 + b4
2. Factorise. (i) 4p2 – 9q2 (ii) 63a2 – 112b2 (iii) 49x2 – 36 (iv) 16x5 – 144x3 (v) (l + m)2 – (l – m)2 (vi) 9x2 y2 – 16 (vii) (x2 – 2xy + y2 ) – z2 (viii) 25a2 – 4b2 + 28bc – 49c2
3. factorize the expressions. (i) ax2 + bx (ii) 7p2 + 21q2 (iii) 2x3 + 2xy2 + 2xz2 (iv) am2 + bm2 + bn2 + an2 (v) (lm + l) + m + 1 (vi) y (y + z) + 9 (y + z) (vii) 5y2 – 20y – 8z + 2yz (viii) 10ab + 4a + 5b + 2 (ix) 6xy – 4y + 6 – 9x
4 . Factorise. (i) a4 – b4 (ii) p4 – 81 (iii) x4 – (y + z)4 (iv) x4 – (x – z) 4 (v) a4 – 2a2 b2 + b4
5. Factorise the following expressions. (i) p2 + 6p + 8 (ii) q2 – 10q + 21 (iii) p2 + 6p – 16

Division of Algebraic Expressions
Division of a monomial by another monomial
Division of a polynomial by a monomial
Division of Algebraic Expressions Continued (Polynomial ÷ Polynomial)
EXERCISE 14.3
1. Carry out the following divisions. (i) 28x4 ÷ 56x (ii) –36y3 ÷ 9y2 (iii) 66pq2 r3 ÷ 11qr2 (iv) 34x3 y3 z3 ÷ 51xy2 z3 (v) 12a8 b8 ÷ (– 6a6 b4 )
2. Divide the given polynomial by the given monomial. (i) (5x2 – 6x) ÷ 3x (ii) (3y8 – 4y6 + 5y4 ) ÷ y4 (iii) 8(x3 y2 z2 + x2 y3 z2 + x2 y2 z3 ) ÷ 4x2 y2 z2 (iv) (x3 + 2x2 + 3x) ÷ 2x (v) (p3 q6 – p6 q3 ) ÷ p3 q3
3. Work out the following divisions. (i) (10x – 25) ÷ 5 (ii) (10x – 25) ÷ (2x – 5) (iii) 10y(6y + 21) ÷ 5(2y + 7) (iv) 9x2 y2 (3z – 24) ÷ 27xy(z – 8) (v) 96abc(3a – 12) (5b – 30) ÷ 144(a – 4) (b – 6)
4. Divide as directed. (i) 5(2x + 1) (3x + 5) ÷ (2x + 1) (ii) 26xy(x + 5) (y – 4) ÷ 13x(y – 4) (iii) 52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p) (iv) 20(y + 4) (y2 + 5y + 3) ÷ 5(y + 4) (v) x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)
5. factorize the expressions and divide them as directed. (i) (y2 + 7y + 10) ÷ (y + 5) (ii) (m2 – 14m – 32) ÷ (m + 2) (iii) (5p2 – 25p + 20) ÷ (p – 1) (iv) 4yz(z2 + 6z – 16) ÷ 2y(z + 8) (v) 5pq(p2 – q2 ) ÷ 2p(p + q) (vi) 12xy(9x2 – 16y2 ) ÷ 4xy(3x + 4y) (vii) 39y3 (50y2 – 98) ÷ 26y2 (5y + 7)

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