Question

plss send me some question of factorisation for practice..​

Answer 1

Answer:

Factorise: 54x2 + 42x3 – 30x4

Factorise: 2x2yz + 2xy2z + 4xyz.

Factorise: 30xy – 12x + 10y– 4.

Regroup the terms and factorise: z – 19 + 19xy – xyz.

Factorise: 100x2 – 80xy + 16y2

Factorise: 16x4 – y4

Factorise: x2 + 6x + 8.

Factorise: 49y2 – 1.

Express the following as in the form of (a+b)(a-b)

(i) a2 – 64

(ii) 20a2 – 45b2

(iii) 32x2y2 – 8

(iv) x2 – 2xy + y2 – z2

(v) 49x2 – 1

Step-by-step explanation:

I hope these questions might help you.

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Answer 2

Answer:

Question 1

Factor the given expressions using identity:

(x+y)2= x2 +y2 +2xy

(x-y)2= x2 +y2 -2xy

x2 –y2 = (x-y) (x+y)

(i) p2 + 6p + 9

(ii) 4z2 – 4z + 1

(iii) 4p4 + 9p4 + 12p2q2

(iv) (a4 - 8a2b2 + 16b4) - 81

(v) 625 – x2 – 2xy – y2

(i) p2 + 6p + 9= (p+3)2

(ii) 4z2 – 4z + 1=(2z+1)2

(iii) 4p4 + 9p4 + 12p2q2=(2p2+ 3q2)2

(iv) (a4 - 8a2b2 + 16b4) - 81=(a2-4b2)2

(v) 625 – x2 – 2xy – y2= 625 -(x2+ 2xy + y2) =(25-x-y)(25+x+y)

Question 2

Divide as directed.

(i) 5(x + 1) (2x + 5) ÷ (2x + 5)

(ii) 39x(x + 5) (y - 2) ÷ 13x(y - 2)

(iii) 12pq (p + q) (q + r) (r + p) ÷ 6pq(q + r) (r + p)

(iv) 60(y - 4) (y2 + 5y + 3) ÷ 5(y - 4)

(v) x(x + 1) (x - 2) (x + 3) ÷ x(x - 2)

i) 5(x+1)

ii) 3(x+5)

iii) 2(p+q)

iv) 5(y2 + 5y + 3)

v) (x+1)(x+3)

Question 3

Factorize the expressions.

(i) px² + qx

(ii) 7x² + 21y²

(iii) 2x³ + 2xy² + 2xz²

(iv) ap² + bq² + bp² + aq²

(v) nm + n2 + m + n

(vi) y (y - z) + 16 (y - z)

(vii) 5y² – 20y – 8z + 2yz

(viii) 10xy + 4x+ 5y + 2

(ix) 6xy - 4y + 6 - 9x

i) x(px+q)

ii) 7(x²+3y²)

iii) 2x(x²+y²+z²)

iv) (a+b)(p²+q²)

v) (n+1)(m+n)

vi) (y-z)(y+16)

vii) 5y² – 20y – 8z + 2yz=5y(y-4) +2z(y-4)=(y-4)(5y+2z)

viii)10xy + 4x+ 5y + 2=2x(5y+2) + 1(5y+2)=(2x+1)(5y+2)

ix) 6xy - 4y + 6 - 9x= 6xy-9x- 4y+6= 3x(2y-3)-2(2y-3)= (3x-2)(2y-3)

Question 4

 Factor completely using the formula:

(i) 576 - p2 + 8pq - 16q2

(ii) 25x2 - (y + z)2

(iii) 4p2 - 4p - 3

(iv) 81 - x2- y2- 2xy

(v) 121 - x2- y2 - 2xy

Solution

i) 576 - p2 + 8pq - 16q2= 242 -(p2 - 8pq + 16q2)=242 -(p-4q)2=(24-p+4q)(24+p-4q)

ii) 25x2 - (y + z)2 =(5x)2-(y + z)2=(5x-y-z)(5x+y+z)

iii) 4p2 - 4p - 3=4p2 - 6p+2p - 3=2p(2p-3) +1(2p-3)=(2p+1)(2p-3)

iv) 81 - x2- y2- 2xy= 92 -(x2+ y2+ 2xy)=92-(x+y)2=(9-x-y)(9+x+y)

v) 121 - x2- y2 - 2xy= 112 -(x2+ y2+ 2xy)=112-(x+y)2=(11-x-y)(11+x+y)

Question 5

Factorize the expressions:

(i) 4a2- 12ab + 9b2

(ii) 36p2- 84pq + 49q2

(iii) 4a8- b8

(iv) (z - 1)2+ 2 (z-1) (2z+3) + (2z +3)2

(v) p2 -9q2

Solution