ML Aggarwal Algebraic Expression and Identities MCQs Class 8 ICSE Ch-10 Maths Solutions

ML Aggarwal Algebraic Expression and Identities MCQs Class 8 ICSE Ch-10 Maths Solutions. We Provide Step by Step Answer of  MCQs Questions for Algebraic Expression and Identities as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-8.

ML Aggarwal Algebraic Expression and Identities MCQs Class 8 ICSE Maths Solutions

Board	ICSE
Publications	Avichal Publishig Company (APC)
Subject	Maths
Class	8th
Chapter-10	Algebraic Expression and Identities
Writer	ML Aggarwal
Book Name	Understanding
Topics	Solution of MCQs
Edition	2023-2024

Algebraic Expression and Identities MCQs

ML Aggarwal Class 8 ICSE Maths Solutions

Page-186

Mental Maths

Question 1. Fill in the blanks:

(i) A symbol which has a fixed value is called a ……….
(ii) A symbol which can be given various numerical values is called ……….. or ………
(iii) The various parts of an algebraic expression separated by + or – sign are called ………..
(iv) An algebraic expression having ………… terms is called a binomial.
(v) Each of the quantity (constant or literal) multiplied together to form a product is called a ………… of the product.
(vi) The terms having the same literal coefficients are called a ………… otherwise they are called …………
(vii) Degree of the polynomial is the greatest sum of the powers of ………… in each term.
(viii)An identity is equality which is true for ………… of variables in it.
(ix) (a + b)² = …………
(x) (x + a) (x + b) = x² + ………… + ab.
(xi) Dividend = ………… + remainder.

Answer:

(i) A symbol which has a fixed value is called a constant
(ii) A symbol which can be given various numerical values is called variable or literal
(iii) The various parts of an algebraic expression separated by + or – sign are called terms
(iv) An algebraic expression having two terms is called a binomial.
(v) Each of the quantity (constant or literal) multiplied together to form a product is called a factor of the product.
(vi) The terms having the same literal coefficients are called a like terms otherwise they are called unlike terms.
(vii) Degree of the polynomial is the greatest sum of the powers of variables in each term.
(viii)An identity is equality which is true for all value of variables in it.
(ix) (a + b)² = a² + 2ab + b²
(x) (x + a) (x + b) = x² + (a + b)x + ab.
(xi) Dividend = divisor x quotient + remainder.

Question 2. State whether the following statements are true (T) or false (F):

(i) An algebraic expression having only one term is called a monomial.
(ii) A symbol which has fixed value is called a literal.
(iii) The term of an algebraic expression having no literal factor is called its constant term,
(iv) In any term of an algebraic expression the constant part is called literal coefficient of the term.
(v) An algebraic expression is called polynomial if the powers of the variables involved in it in each term are non-negative integers.
(vi) 5x²y²z, 3x²zy², – 4/5 zx²y² are unlike terms.
(vii) 5x + 2/𝑥 + 7 is a polynomial of degree 1.
(viii) 3x²y + 7x + 8y + 9 is a polynomial of degree 3.
(ix) Numerical coefficient of -7x³y is 7.

(x) xyz + yzx + zey is a monomial
(xi) An equation is true for all values of variables in it.
(xii) (a – b)² + 2ab = a² + b².

Answer:

(i) An algebraic expression having only one term is called a monomial. True
(ii) A symbol which has fixed value is called a literal. False
(iii) The term of an algebraic expression having no literal factor is called its constant term. True
(iv) In any term of an algebraic expression the constant part is called literal coefficient of the term. False
(v) An algebraic expression is called polynomial if the powers of the variables involved in it in each term are non-negative integers. True
(vi) 5x²y²z, 3x²zy², – 4/5 zx²y² are unlike terms. False
(vii) 5x + 2/𝑥 + 7 is a polynomial of degree 1. False
(viii) 3x²y + 7x + 8y + 9 is a polynomial of degree 3. True
(ix) Numerical coefficient of -7x³y is 7. False

(x) xyz + yzx + zey is a monomial. True
(xi) An equation is true for all values of variables in it. False
(xii) (a – b)² + 2ab = a² + b². True

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Algebraic Expression and Identities MCQs

ML Aggarwal Class 8 ICSE Maths Solutions

Page-187

choose the correct answer from the given four option (3 to 18)

Question 3. The literal coefficient of -9xyz² is

(a) -9
(b) xy
(c) xyz²
(d) -9xy

Answer: correct options is (c) xyz²

Question 4. Which of the following algebraic expression is

(a) 3x² – 2x + 7
(b) 5𝑥3/2𝑥 + 3x² + 8
(c) 3x + 2/𝑥 + 7
(d) √2x² + √3x + √6

Answer: correct options is (c) 3x + 2/𝑥 + 7

Question 5. Which of the following algebraic expressions is not a monomial?

(a) 3x × y × z
(b) -5pq
(c) 8m² × n ÷ 31
(d) 7x ÷ y – z

Answer: correct options is (d) 7x ÷ y – z

Question 6. Degree of the polynomial 7x²yz² + 6x³y²z² – 5x + 8y is

(a) 4
(b) 5
(c) 6
(d) 7

Answer: correct options is (d) 7

(ML Aggarwal Algebraic Expression and Identities MCQs Class 8)

Question 7. a(b -c) + b(c – a) + c(a – b) is equal to

(a) ab + bc + ca
(b) 0
(c) 2(ab + bc + ca)
(d) none of these

Answer: correct options is (b) 0

Question 8. 7xy/5 – 2xy/3 +  8xy/9 is equal to

(a) (73/45)xy
(b) – (73/45)xy
(c) xy
(d) none of these

Answer: correct options is (a) (73/45)xy

Question 9. (3p²qr³) × (-4p³q²r²) x (7pq³r) is equal to

(a) 84p⁶q⁶r⁶
(b) -84p⁶q⁶r⁶
(c) 84p⁶q⁵r⁶
(d) -84p⁶q⁵r⁶

Answer: correct options is (d) -84p⁶q⁵r⁶

Question 10. 3m × (2m² – 5mn + 4n²) is equal to

(a) 6m³ + 15m²n – 12mn²
(b) 6m³ – 15m²n + 12mn²
(c) 6m³ – 15m²n – 12mn²
(d) 6m³ + 15m²n + 12mn²

Answer: correct options is (b) 6m³ – 15m²n + 12mn²

Question 11. Volume of a rectangular box whose adjacent edges are 3x²y, 4y²z and 5z²x respectively is

(a) 60xyz
(b) 60x²y²z²
(c) 60x³y³z³
(d) none of these

Answer: correct options is (c) 60x³y³z³

Question 12. (x – 1) (x + 2) is equal to

(a) 2x + 3
(b) x² + 2x + 2
(c) x² + 3x + 2
(d) x² + 2x + 3

Answer: correct options is (c) x² + 3x + 2

Question 13. If x + 1/𝑥 = 2, then x² + 1/𝑥2 is equal to

(a) 4
(b) 2
(c) 0
(d) none of these

Answer: correct options is (b) 2

Question 14. If x² + y² = 9 and xy = 8, then x + y is equal to

(a) 25
(b) 5
(c) -5
(d) ±5

Answer: correct options is (d) ±5

Question 15. (102)² – (98)² is equal to

(a) 200
(b) 400
(c) 600
(d) 800

Answer: correct options is (d) 800

(ML Aggarwal Algebraic Expression and Identities MCQs Class 8)

Question 16. -50x³y²z² divided by -5xyz is equal to

(a) 10xyz
(b) 10x²yz
(c) -10xyz
(d) -10x²yz

Answer: correct options is (b) 10x²yz

Question 17. 96 × 104 is equal to

(a) 9984
(b) 9974
(c) 9964
(d) none of these

Answer: correct options is (a) 9984

Question 18. If the area of a rectangle is 24(x²yz + xy²z + xyz²) and its length is 8xyz, then its breadth is

(a) 3(x + y + z)
(b) 3xyz
(c) 3(x + y – z)
(d) none of these

Answer: correct options is (a) 3(x + y + z)

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Algebraic Expression and Identities MCQs

ML Aggarwal Class 8 ICSE Maths Solutions

Page-188

Higher Order Thinking Skills ( HOTS )

Question 1. Find the polynomial that represents the product of three consecutive odd integers, the smallest being (2x – 1).

Answer:

Let the odd numbers be 2x-1 , 2x+1 , 2x+ 3

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

= (2x)²-1²(2x+3)

= 4x²-1(2x+3)

= 4x²(2x) +3(4x²)-2x-3

= 8x³ + 12x² -2x-3

Question 2. Using the identity (a + b) = a² + 2ab + b², derive the formula for (a + b + c)². Hence, find the value of (2x – 3y + 4z)².

Answer:

( a + b )² = a² + 2 a b + b² , We find value of ( a + b + c )² by using given identity ,

⇒[ ( a + b ) + c ]²   , Now we use given identity and get :

⇒( a + b )² + 2 ( a + b ) ( c )  + c²

⇒( a + b )² + 2 a c + 2 b c + c²

⇒a² + 2 a b + b² + 2 c a+ 2 b c + c²

⇒a² + b² + c² + 2 a b + 2 b c  + 2 c a

( a + b + c )² = a² + b² + c2 + 2 a b + 2 b c  + 2 c a

Now we use above formula to get value of ( 2 x – 3 y + 4 z )² ,As :

⇒[ 2 x + ( – 3 y ) + 4 z ]2

⇒ ( 2 x )² + ( – 3 y )² + ( 4 z )² + 2 ( 2 x )( – 3 y ) + 2 ( – 3 y ) ( 4 z )  + 2 ( 4 z ) ( 2 x )

⇒ 4 x ² + 9 y ² + 16 z ²  – 12  x y  – 24  y z + 16 z  x

Question 3. Using the product of algebraic expressions, find the formulas for (a + b)³ and (a – b)³.

Answer:

(a+b)³ =  a³ + 3a²b + 3ab² + b³

Derivation of the (a+b)³

To find the cube of a binomial,

we will just multiply (a + b)(a + b)(a + b). (a + b)³ formula is also an identity.

It holds true for every value of a and b.

The (a + b)³ is given as,

(a + b)³ = (a + b)(a + b)(a + b)

= (a² + 2ab + b²)(a + b)

= a³ + a²b + 2a²b + 2ab² + ab² + b³

= a³ + 3a²b + 3ab² + b³

= a³ + 3ab(a+b) + b³

Hence, (a + b)³ formula is:

(a + b)³ = a³ + 3a²b + 3ab² + b³.

(a – b)³ = (a – b)(a – b)(a – b)

= (a² – 2ab + b²)(a – b)

= a³ – a²b – 2a²b + 2ab² + ab² – b³

= a³ – 3a²b + 3ab² – b³

= a³ – 3ab(a-b) – b³

Therefore, (a – b)³ formula is:

(a – b)³ = a³ – 3a²b + 3ab² – b³

— End of Algebraic Expression and Identities MCQs Class 8 ICSE Maths Solutions :–

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