NCTB Class 6 Math Chapter Four Exercise 4.3 Solution by Math Expert. Bangladesh Board Class 6 Math Solution Chapter 4 “Algebraic Expressions’’ Exercise 4.3 Solution.

Board |
NCTB |

Class |
6 |

Subject |
Mathematics |

Chapter |
4 |

Chapter Name |
“Algebraic Expressions’’ |

Exercise |
4.3 Solution |

**Exercise:- 4.3**

**(1) Which one of the following is the coefficient of x in 5x+3y?**

**Solution:- **

In 5x+3y, the coefficient of x is (d) 5

**(2)Which one of the following is the sum of three times of x and two times of y?**

**Solution:- **

(b) 3x+2y

**(3) Which one is the index of x in 7x ^{3} X x^{2}?**

**Solution:- **

In 7x^{3} X x^{2} = 7x^{2}

Therefore, index of x is (b) 5

**(4) Which one of the following indicates a pair of similar terms?**

**Solution:- **

Pair of similar terms (c) 3x^{2}, -7x^{2}

**(5) If m=-6 in expression m ^{2}-7, what is the value of the expression?**

** Solution:- **

M = 6;

M^{2}-7

= (-6)^{2} -7

= 36-7

= 29

(d) 29.

**(6) If you Subtract b-a, what is difference?**

** Solution:- **

(a-b)- (b-a)

= a-b-b +a

= 2a-2b

(c) 2a-2b.

**(7) What is the sum of three expressions x ^{2}+3, x^{2}-2, -2x^{2}+1?**

**Solution:- **

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

= x^{2}+3-x^{2}-2-2x^{2}+1

= 2

**(8) In the expressions 5x ^{4}**

**Solution:- **

(b) (i) and (iii) correct.

**(9) In x and y variables—**

**Solution:- **

(i) (a) (i) and (ii) correct.

**(10) If x=2 and y=-3, what is the value of the first expression?**

**Solution:- **

Here, x=2, y= -3;

Therefore, x^{2}-y^{2}

= (x+y) (x-y)

= (2-3) (2+3)

= (-1) (5)

= -5

(b) -5 (Answer)

**(11) What is the sum of the three expressions?**

**Solution:- **

X^{2}-y^{2}+y^{2}-z^{2}+z^{2}-x^{2}

= 0

**(12) (i) 12x is the sum of x and the power of 12 **

**(ii) The index of a is 3 in expression 4a ^{3}**

**(iii) The coefficient of x in the basis of above information?**

**Solution:- **

(c) & (iii) are correct.

**(14) 9x ^{2}, 8x^{2}, 5y^{2} are three algebraic expressions then—**

**(a) What is the sum of numerical coefficients of three expressions?**

**Solution:- **

9+8+5

= 22

(d) 22 (Answer)

**(b) What is the index of the product of the two expression?**

**Solution:- **

(a) 4 (Answer)

**(15) x ^{2}+y^{2}+z^{2}, x^{2}+y^{2}z^{2}, -x^{2}+y^{2}-z^{2 }are three algebraic expressions. On the basis of this information, answer the following questions (1) to (4) **

**(1) Which one will be the sum of difference of the first two expressions with the third expression?**

**Solution:- **

x^{2}+y^{2}+z^{2 }x^{2}-y^{2}+z^{2 }-(- x^{2}+y^{2}-z^{2})

= x^{2}+y^{2}+z^{2 }x^{2}-y^{2}+z^{2}+ x^{2}-y^{2}-z^{2}

= 3 x^{2}-y^{2}+3z^{2}

(b) 3 x^{2}-y^{2}+3z^{2} (Answer)

**(2) What is the coefficient of y ^{2} in the second expression?**

**Solution:-**

(b) -1 (Answer)

**(3) What is the sum of the three expressions?**

**Solution:-**

x^{2}+y^{2}+z^{2}+ x^{2}-y^{2}+z^{2}– x^{2}+y^{2}-z^{2}

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

(c) x^{2}+y^{2}+z^{2} (Answer)

**(4) Which is the sum of the three expressions?**

**Solution:- **

(b) (Answer)

**Add (16-25):**

**(16) 3a+4b, a+3b**

= 4a+7b

**(17) 2a+ 3b+ 3a+ 5b+ 5a+ 6b**

= 10a+ 14b

**(18) 4a-3b+(-3a+b) + 2a+3b**

= 4a-3b-3a+b+2a+3b

= 3a+b

**(19) 7x+ 5y+ 2z+3x- 6y+7z- 9x+4y +z**

= x- 3y+10z

**(20) X ^{2}+xy+z+3x^{2}-2xy+3z+2x^{2}+7xy-2z**

= 6x^{2}+ 6xy- 2z

= 2 (3x^{2}+ 3xy- z) (Answer)

**(21) 4p ^{2}+7q^{2}+4r^{2}+p^{2}+3r^{2}+8q^{2}-7p^{2}-r^{2}**

**= -2p ^{2}+ 15q^{2 }+6r^{2} (Answer)**

**(22) 3a +2b- 6c- 5b +4a+ 3c+ 8b -6a +4c**

= a+5b +c (Answer)

**(23) 2x ^{3}-9x^{2}+11x+ 5-x^{3}+7x^{2 }-8x-3-x^{3}+2x^{2 }-4x+1**

= -x+3 (Answer)

**(24) 5ax+ 3by- 14cz- 11by -7ax- 9cz +3ax+ 6by- 8cz**

= a x- 31cz -2by (Answer)

**(25) x ^{2}-5x+6+x^{2}+3x-2-x^{2}+x+1-x^{2}+6x-5**

= 5x (Answer)

**(26) L.H.S, a ^{2}+b^{2}+c^{2}**

= x^{2}+y^{2 }-z^{2}+y^{2}+ z^{2 }–x^{2}+ x^{2}-y^{2}

= x+ y+ z

R.H.S

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

**(27) L.H.S, x+ y+ z**

= 5a+7b + 9c+b- 3a-4c +c-2b+a

=3a+ 6b+ 6c

= 3 (a+ 2b+ 2c)

= R.H.S

= R.H.S =L.H.S (Proved)

**Subtract (28-35):**

(36) **Solution:- **

L.H.S, a+ b-c

= x^{2}+z^{2}+y^{2}+z^{2}-x^{2}-y^{2}

= 2z^{2}

= R.H.S

Therefore = R.H.S (proved)

(37) **solution:**

L.H.S, x-y +z

= a+ b -b- c+ c+ a

= 2a

= R.H.S

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

(38) **Solution:- **

L.H.S, x-y+ z

= a+ b +c-a +b +c +b- c +a

= a+ 3b +c

= R.H.S

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

(39) **Solution:- **

(a) Numerical co-officient of b^{2} is a 1.

(b) 2a^{2}+3c^{2}

(c) 3a^{2}-2b^{2}+4c^{2} (Answer)

(40) **Solution:-** (a) Total price

= (3Xx+2xy) Rs

= (3x+2y) Rs

(b)**Solution:-** Total price of 5 note book & 8 pencils = (5x+8z) Rs.

Therefore, Algebraic expression [(5x+8z)- 10y]

(c) **Solution:-** Numeric co-offcient y & z are -2 &5.

Product of numerical co-officient

= 3x (-2) x 5

= -30 (Answer)

(41) (a) **Solution:-** There are three terms in the first expression.

That’s are—5x^{2}, x y, 3y^{2}

(b) **Solution:-**5x^{2}+xy+3y^{2}

X^{2}-8xy+0

-x^{2}+ 10xy +y^{2}

5x^{2}+ 3xy +4y^{2}

Therefore, Co-officent of x y is 3.

(c)** Solution:-**(5x^{2}+xy+3y^{2}) – (x^{2}-8xy) – (y^{2}-x^{2}+10xy)

= 5x^{2}+ x y+ 3y^{2}-x^{2}+8xy –y^{2}+x^{2}-10xy

= 5x^{2}-xy+2y^{2}

When, x=2: y=1

Therefore, 5x (2^{2}) – 2×1 + 2×1^{2}

= 5×4-2+2

= 20 (Answer)