Ex - 7.1, Algebraic Expressions, Class 7, Math RD Sharma Solutions | RD Sharma Solutions for Class 7 Mathematics PDF Download

Question 1:

Identify the monomials, binomials, trinomials and quadrinomials from the following expressions:
 (i) a²
 (ii) a² − b²
 (iii) x³ + y³ + z³
 (iv) x³ + y³ + z³ + 3xyz
 (v) 7 + 5
 (vi) abc + 1
 (vii) 3x − 2 + 5
 (viii) 2x − 3x + 4
 (ix) xy + yz + zx
 (x) ax³ + bc² + cx + d

Answer 1:

The monomials, binomials, trinomials and quadrinomials are as follows.
(i) a² is a monomial expression as it contains one term only.
(ii) a² - b² is a binomial expression as it contains two terms.
(iii) x³ + y³ + z³ is a trinomial expression as it contains three terms.
(iv) x³ + y³ + z³ + xyz is a quadrinomial expression as it contains four terms.
(v) 7 + 5 = 12 is a monomial expression as it contains one term only.
(vi) abc +1 is a binomial expression as it contains two terms.
(vii) 3x - 2 + 5 = 3x + 3 is a binomial expression as it contains two terms.
(viii) 2x - 3y + 4 is a trinomial expression as it contains three terms.
(ix) xy + yz + zx is a trinomial expression as it contains three terms.
(x) ax³ +bx² +cx + d is a quadrinomial expression as it contains four terms.

Question 2:

Write all the terms of each of the following algebraic expressions:
 (i) 3x
 (ii) 2x − 3
 (iii) 2x² − 7
 (iv) 2x² + y² − 3xy + 4

Answer 2:

The terms of each of the given algebraic expressions are as follows.
(i) 3x is the only term of the given algebraic expression.
(ii) 2x and -3 are the terms of the given algebraic expression.
(iii) 2x² and -7 are the terms of the given algebraic expression.
(iv) 2x², y², -3xy  and 4 are the terms of the given algebraic expression.

Question 3:

Identify the like terms and also mention the numerical coefficients of those terms:

(i) 4xy, −5x²y, −3yx, 2xy²

Answer 3:

like terms	Numerical Cofficients

Question 4:

Identify the like terms in the following algebraic expressions:

(i) a²+b²−2a²+c²+4a

(ii) 3x+4xy−2yz+5/2zy
(iii) abc+ab²c+2acb²+3c²ab+b²ac−2a²bc+3cab²

Answer 4:

The like terms in the given algebraic expressions are as follows.
(i) The like terms in the given algebraic expression are a²  and -2a².

(ii) The like terms in the given algebraic expression are −2yz and 52zy-2yz and 5/2zy.
(iii) The like terms in the given algebraic expression are ab²c, 2acb², b²ac and 3cab².

Question 5:

Write the coefficient of x in the following:
 (i) −12x
 (ii) −7xy
 (iii) xyz
 (iv) −7

Answer 5:

 The coefficients of x are as follows.
(i) The numerical coefficient of x is -12.
(ii) The numerical coefficient of x is -7y.
(iii) The numerical coefficient of x is yz.
(iv) The numerical coefficient of x is -7a.

Question 6:

Write the coefficient of x² in the following:
 (i) −3x²
 (ii) 5x²yx

Answer 6:

The coefficients of x² are as follows.
 (i) The numerical coefficient of x² is -3.
(ii) The numerical coefficient of x² is 5yz.

(iii) The numerical coefficient of x² is 5/7z.
(iv) The numerical coefficient of x² is −3/2a.

Question 7:

Write the coefficient of:
 (i) y in −3y
 (ii) a in 2ab
 (iii) z in −7xyz
 (iv) p in −3pqr
 (v) y² in 9xy²z
 (vi) x³ in x³ + 1
 (vii) x² in −x²

Answer 7:

 The coefficients are as follows.

 (i) The coefficient of  y is -3.
 (ii) The coefficient of  a is 2b.
 (iii) The coefficient of  z is -7xy.
 (iv) The coefficient of  p is -3qr.
 (v) The coefficient of  y² is 9xz.
 (vi) The coefficient of  x³ is 1.
 (vii) The coefficient of  -x² is - 1.

Question 8:

Write the numerical coefficient of each of the following:
 (i) xy
 (ii) −6yz
 (iii) 7abc
 (iv) −2x³y²z

Answer 8:

The numerical coefficient of each of the given terms is as follows.
(i) The numerical coefficient in the term xy is 1.
(ii) The numerical coefficient in the term -6yz is - 6.
(iii) The numerical coefficient in the term 7abc is 7.
(iv) The numerical coefficient in the term -2x³y²z is - 2.

Question 9:

Write the numerical coefficient of each term in the following algebraic expressions:

Answer 9:

The numerical coefficient of each term in the given algebraic expressions is as follows.

Term	Coefficient

Question 10:

Write the constant term of each of the following algebraic expressions:
 (i) x²y − xy² + 7xy − 3
 (ii) a³ − 3a² + 7a + 5

Answer 10:

The constant term of each of the given algebraic expressions is as follows.
(i) The constant term in the given algebraic expression is -3.
(ii) The constant term in the given algebraic expression is 5.

Question 11:

Evaluate each of the following expressions for x = − 2, y = −1, z = 3:

Answer 11:

We have x = −2, y = −1 and z = 3.
Thus,
(i)

(ii) x² + y² + z²- xy - yz - zx
     = (-2)² + (-1)² + (3)² - (-2)(-1) - (-1)(3) - (3)(-2)
     = 4 + 1 + 9 - 2 + 3 + 6
     = (4 + 1 + 9 + 3 + 6) - 2
     = 23 - 2 = 21

Question 12:

Evaluate each of the following algebraic expressions for x = 1, y = −1, z = 2, a = −2, b = 1, c = −2:

(i) ax + by + cz
 (ii) ax² + by² − cz²
 (iii) axy + byz + cxy

Answer 12:

We have x = 1, y = −1, z = 2, a = −2, b = 1 and c = −2.
Thus,
(i) ax + by + cz
    = (-2)(1) + (1)(-1) + (-2)(2)
    = - 2 + (- 1) + (- 4)
    = - 2 -1 - 4 = -7

(ii) ax² + by² - cz²
    = (-2)(1)² + (1)(-1)² - (-2)(2)²
    = -2 x 1 + 1 - (-2 x 4)
    = -2 + 1 - (-8)
    = -2 + 1 + 8
    = -2 + 9
    = 7

(iii) axy + byz + cxy
     = (-2)(1)(-1) + (1)(-1)(2) + (-2)(1)(-1)
     = 2 + (-2) + 2
     = 2 - 2 + 2
     = 4 - 2
     = 2