IDENTIFY INOT MONOMIAL BINOMIAL AND TRINOMIAL

Classify the following polynomials based on number of terms.

Problem 1 :

4y – 7z

Solution :

4y – 7z

Number of terms = 2

So, 4y – 7z is a binomial.

Problem 2 :

y²

Solution :

y²

Number of terms = 1

So, y² is a monomial.

Problem 3 :

x + y - xy

Solution :

x + y - xy

Number of terms = 3

So, x + y - xy is a trinomial.

Problem 4 :

100

Solution :

100

Number of terms = 1

So, 100 is a monomial.

Problem 5 :

ab – a - b

Solution :

ab - a - b

Number of terms = 3

So, ab - a - b is a trinomial.

Problem 6 :

5 – 3t

Solution :

5 – 3t

Number of terms = 2

So, 5 – 3t is a binomial.

Problem 7 :

4p²q – 4pq²

Solution :

4p²q – 4pq²

Number of terms = 2

So, 4p²q – 4pq² is a binomial.

Problem 8 :

7mn

Solution :

7mn

Number of terms = 1

So, 7mn is a monomial.

Problem 9 :

z² – 3z + 8

Solution :

z² – 3z + 8

Number of terms = 3

So, z² – 3z + 8 is a trinomial.

Problem 10 :

a² + b²

Solution :

a² + b²

Number of terms = 2

So, a² + b² is a binomial.

Problem 11 :

z² + z

Solution :

z² + z

Number of terms = 2

So, z² + z is a binomial.

Problem 12 :

1 + x + x²

Solution :

1 + x + x²

Number of terms = 3

So, 1 + x + x² is a trinomial.

Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.

Problem 1 :

3x²yz² – 3xy²z + x²yz² + 7xy²z

Solution :

Given, 3x²yz² – 3xy²z + x²yz² + 7xy²z

= (3x²yz² + x²yz²) + (7xy²z – 3xy²z)

= (3 + 1) x²yz² + (7 – 3) xy²z

= 4x²yz² + 4xy²z

So, the expression is binomial.

Problem 2 :

x⁴ + 3x³y + 3x²y² – 3x³y – 3xy³ + y⁴ – 3x²y²

Solution :

x⁴ + 3x³y + 3x²y² – 3x³y – 3xy³ + y⁴ – 3x²y²

= 3x³y – 3x³y + 3x²y² – 3x²y² – 3xy³ + x⁴ + y⁴

= – 3xy³ + x⁴ + y⁴

So, the expression is trinomial.

Problem 3 :

p³q²r + pq²r³ + 3p²qr² – 9p²qr²

Solution :

p³q²r + pq²r³ + 3p²qr² – 9p²qr²

= p³q²r + pq²r³ – 6p²qr²

So, the expression is trinomial.

Problem 4 :

2a + 2b + 2c – 2a – 2b – 2c – 2b + 2c + 2a

Solution :

2a + 2b + 2c – 2a – 2b – 2c – 2b + 2c + 2a

= (2a – 2a + 2a) + (2b – 2b – 2b) + (2c – 2c + 2c)

= 2a – 2b + 2c

So, the expression is trinomial.

Problem 5 :

50x³ – 21x + 107 + 41x³ – x + 1 – 93 + 71x – 31x³

Solution :

= 50x³ – 21x + 107 + 41x³ – x + 1 – 93 + 71x – 31x³

= (50x³ + 41x³ – 31x³) + (-21x – x + 71x) + (107 + 1 – 93)

= 60x³ + 49x + 15

So, the expression is trinomial.