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Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial. x⁴ + 3x³y + 3x²y² - 3x³y - 3xy³ + y⁴ - 3x²y²

Solution:

Given, the expression is x⁴ + 3x³y + 3x²y² - 3x³y - 3xy³ + y⁴ - 3x²y².

We have to combine the like terms and classify the expression.

By combining like terms,

x⁴ + 3x³y + 3x²y² - 3x³y - 3xy³ + y⁴ - 3x²y² = x⁴ + y⁴ - 3xy³ + (3x³y - 3x³y) + (3x²y² - 3x²y²)

By distributive property,

= x⁴ + y⁴ - 3xy³ + (3 - 3)x³y + (3 - 3)x²y²

= x⁴ + y⁴ - 3xy³

Therefore, the simplified expression after combining the like terms is x⁴ + y⁴ - 3xy³.

The expression contains three unlike terms.

Expression with three unlike terms is called a 'Trinomial’.

Therefore, x⁴ + y⁴ - 3xy³ is a trinomial.

✦ Try This: Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial. p⁴ + p³q + p²q² - p³q - 2pq³ + q⁴ + p²q² + r³

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 12

NCERT Exemplar Class 7 Maths Chapter 10 Problem 56 (b)

Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial. x⁴ + 3x³y + 3x²y² - 3x³y - 3xy³ + y⁴ - 3x²y²

Summary:

After simplifying the expression x⁴ + 3x³y + 3x²y² - 3x³y - 3xy³ + y⁴ - 3x²y² by combining the like terms we get x⁴ + y⁴ - 3xy³, which is a trinomial.

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