NCTB Class 6 Math Chapter Four Exercise 4.2 Solution by Math Expert. Bangladesh Board Class 6 Math Solution Chapter 4 “Algebraic Expressions’’ Exercise 4.2 Solution.

Board |
NCTB |

Class |
6 |

Subject |
Mathematics |

Chapter |
4 |

Chapter Name |
“Algebraic Expressions’’ |

Exercise |
4.2 Solution |

**Exercise:- 4.2**

**Exercise:- 4.2**

**(1) Simplify:**

**Solution:- **

**(i) x ^{3} X x^{7}**

= x^{10}

**(ii) a ^{3} x a x a^{5}**

= a^{9}

**(iii) x ^{4} X x^{2}X x^{9}**

=x^{15}

**(iv) m x m ^{2} x n^{3} x m^{3} x n^{7}**

=m^{6} n^{10}

**(v) 3a x 4b x2a x 5c x3b**

= 360 a^{2} b^{2} c

**(vi) 2x ^{2} X y^{2} X 2z^{2} X 3y^{2} X 4x^{2}**

= 48 x^{4} y^{4} z^{2}

**(2) If a=2, b=3, c=1, find the value of each of the following expressions:**

**Solution:- **

**(i) a ^{3} + b^{2}**

= (2)^{2}+ (3)^{2}

= 8+27

= 35 [Therefore a=2; b=3]

**(ii) b + c**

= 27+1

= 28

**(iii) a ^{2}–b^{2} +c^{2}**

= (2)^{2} – (3)^{2} + (1)^{2}

= 4-9+1

= -5+1

= -4

**(iv) b ^{2}– 2ab+a^{2}**

= (3)^{2} – 2X2X3+ (2)^{2}

= 9-12+4

= -3+4

= 1

**(v) a ^{2} -2ac+c^{2}**

= (2)^{2} – 2X2X1+1^{2}

= 4-4+1

= 1

**(3) If x=3, y=5, z=2, show that **

**Solution:- **

Therefore, L.H.S, **y ^{2}-x^{2}**

= (y+x) (y-x)

= (5+3) (5-3)

= 8×2

= 16

R.H.S, ** (x+y) (y-x)**

= (3+5) (5-3)

= 8×2

= 16

Therefore, L.H.S= R.H.S (proved)

(ii) L.H.S, **(x+y) ^{2}**

= x ^{2}+ 2xy+y^{2}

**= (3) ^{2} + 2x3x5 +5^{2}**

= 9+30+25

= 64

R.H.S, **(x-y) + 4xy**

= (x+y)^{2}

= (3+5)^{2}

= (8)^{2}

= 64

Therefore, L.H.S = R.H.S (proved)

(iii) L.H.S, **(y+z) ^{2}**

= (5+2)^{2}

= (7)^{2}

= 49

R.H.S, **y+2xz+z**

= 5^{2} +2x5x2+2^{2}

= 25+20+4

= 49

Therefore, L.H.S= R.H.S (proved)

(iv) **L.H.S, (x+z) ^{2}**

= (3+2)^{2}

= (5)^{2}

= 25

R.H.S,** x+2xz+z**

= 3^{2}+2x3x2+2^{2}

= 9+12+4

= 25

Therefore, L.H.S= R.H.S (proved)

**(4) Tick the correct answer: **

**Solution:- **

**(i) a ^{7}x a^{8}**

= a^{15} (b)

**(ii) a ^{3} x a^{-3}**

= a^{0}(c)

**(iii) 5x ^{2} X 4x^{4}**

= 20x^{6} (b)

**(iv) x ^{5}X x^{4}**

= x^{9}

**(v) 5a ^{3}X a^{5}**

= 5a^{8}