NCTB Class 8 Math Chapter Four Exercise 4.4 Solution

NCTB Class 8 Math Chapter Four Exercise 4.4 Solutions by Math Expert. Bangladesh Board Class 8 Math Solution Chapter Four Algebraic Formulae and Applications Exercise 4.4 Solution.

Board	NCTB
Class	8
Subject	Mathematics
Chapter	4
Chapter Name	Algebraic Formulae and Applications
Exercise	4.4 Solution

Exercise: 4.4

1> Which of the following is the square of (-5-y)?

= (-5)²-2.(-5).(y)+y²⁼

= 25+10y+y²

2> which one of the following is the product of (x-2) and (4x+3)

(x-2)(4x+3)

= 4x²+3x-8x-6

= 4x²-5x-6

Ans: (a) (d)

3> what is the H.C.F of x²-2x-3 and x²+2x-3

x²-2x-3

= x²-3x+1x-3

= x(x-3)+1(x-3)

= (x-3) (x+1)

4> which of the following will be right if we express (3x-5)(5+3x) in the form of difference between two square:

(3x-5)²-(5+3x)²

= {(3x)²-2.3x.5+5²)-(5)²+2.5x.3x+(3x)²}

= (9x²-30x+25)-(25+30x+9x²)

= 9x²-30x+25-25+30x-9x²

= -60x

8> which one of the following expressions in the factor of x²-x-30 ?

x²-x-30

= x²-6x+5x-30

= x (x-6)+5(x-6)

= (x+5)(x-6) (b) Answer.

9>  If x²-10x+21 and x²-6x-7 are two algebraic expressions –

(a) x²-10x+21

= x²-7x-3x+21

=x(x-7)-3(x-7)

(b) x²-6x-7

= x²+7x-x-7

= x(x+7)-1(x+7)

= (x+7)(x-1)

Product = (x²-10x+21)( x²-6x-7)

= x⁴+6x³-7x²-10³-60x²+70x+21x²+126x-147

None of the following are correct

10> In algebraic formulae:

According to the question the correct answer is (d)

11> If x+y=5 and x-y=3, then

x+y=5;

x-y=3

or, (x-y)²=3²

or, (x+y)²-4xy=9

or, (5)²-4xy=9

or, -4xy = 9-25

= -16

Or, xy=4

 

X²+y²

= (x+y)²-2.xy

= (5)²-2.4

= 25-8

= 17 (c)

(2) The value of xy is = 4

(3) The value of (x²-y²)

= (x+y)(x-y)

= 5 x 3

= 15 (c)

12> If x+1/x=2, then ,

(1) (X-1/x)²

= (x+1/x)²-4.x.1/x

= (2)²-4

= 0

(2) x³+1/x³

= (x+1/x)³-3.x.1/x (x+1/x)

= (2)³-3.2

= 8-6

= 2

 

13> Find the H.C.F of the following :

36a²b²c⁴d⁵, 54a⁵c²d⁴, 90a⁴b³c²

Ans is = 18a²c²

14> 20x³y²a³b⁴, 15x⁴y³a⁴b³ and 35x²y⁴a³b²

Ans is = 5x²y²a³b²

15> 15x²y³z⁴a³, 12x³y²z³a⁴ and 27x³y⁴z⁵a⁷

Ans is = 3x²y²z³a³

16> 18a³b⁴c⁵, 42a⁴c³d⁴, 60b³c⁴d⁵ and 78a²b⁴d³

Ans is = 6

17> x²-3x= x(x-3)

X² – 9 = (x)²-(3)²

= (x+3)(x-3)

X²-4x+3

= x²-3x-x+3

= x(x-3)-1(x-3)

=(x-1)(x-3)

H.C.F of this expressions = (x-3)

18> 18 (x+y)³, 24(x+y)², 32(x²-y²)

1^st expression , 18(x+y)³⁼

2^nd expression , 24(x+y)²

3^rd expression, 32(x²-y²)

Therefore H.C.F is = 2(x+y).

20>

1^st, a³-3a²-10a

= a(a²-3a-10)

= a(a²-5a+2a-10)

= a {a(a-5)+2(a-5)}

= a (a-5)(a+2)

2^nd, a³+6a²+8a

= a(a²+6a+8)

= a(a²+4a+2a+8)

= a {a(a+4)+2(a+4)}

= a (a+4)(a+2)

3^rd, a⁴-5a³-14a²

= a²(a²-5a-14)

= a²(a²-7a+2a-14)

= a²{a(a+7)+2(a-7)}

= a²(a-7)(a+2)

H.C.F is = a(a+2)

21> 1^st, a⁵b²c

2^nd, ab³c²

3^rd, a⁷b⁴c³

Therefore, L.C.M is = a⁷b⁴c³

22> 1^st, 5a²b³c²

2^nd, 10ab²c³

3^rd, 15ab³c

Therefore, L.C.M is = 30a²b³c³

23> 1^st, 3x³y²

2^nd, 4xy³z

3^rd, 5x⁴y²z²

4^th, 12xy⁴z²

Therefore, L.C.M is = 120x⁴y⁴z²

24> 1^st, 3a²d³; 2^nd, 9d²b²; 3^rd, 12c³d²; 4^th, 24a³b²; 5^th, 35c³d²

Therefore, L.C.M is 72a³b²c³d³

25> 1^st, x²+3x+2

= x²+2x+x+2

= x(x+2)+1(x+2)

= (x+2)(x+1)

2^nd, x²-1

= (x+1)(x-1)

3^rd, x²+x-2

= x²+2x-x-2

= x(x+2)-1(x+2)

= (x-1)(x+2)

Therefore, L.C.M is (x+2)(x+1)(x-1)

26> 1^st term, x²-4= x²-2²=(x+2)(x-2)

2^nd, x²+4x+4

= x²+2x+2x+4

= x(x+2)+2(x+2)

= (x+2)²

3^rd, x³-8 = x³-2³

= (x-2)(x²+2x+4)

Therefore, L.C.M is (x+2)²(x-2)(x²+2x+4)

27> 1^st, 6x²-x-1

= 6x²-3x+2x-1

= 3x (2x-1)+1(2x-1)

= (3x+1)(2x-1)

2^nd, 3x²+7x+2

= 3x²+6x+x+2

= 3x(x+2)+1(x+2)

= (3x+1)(x+2)

3^rd, 2x²+3x-2

= 2x²+4x-x-2

= 2x (x+2)-1(x+2)

= (2x-1)(x+2)

Therefore, L.C.M is (3x+1)(2x-1)(x+2)

29> x²+ 1/x²=3

Or, (x+1/x)²-2.x.1/x =3

Or, (x+1/x)²-2 =3

 

(b) x⁶+1/x³

= x³+1/x³

= (x+1/x)³-3.x.1/x (x+1/x)

= – 3

= 2