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Mathematics

Consider the expression 32x2y−12xy2+6x2y2\dfrac{3}{2}x^2y - \dfrac{1}{2}xy^2 + 6x^2y^2

(i) How many terms are there? What do you call such an expression?

(ii) List out the terms.

(iii) In the term −12xy2-\dfrac{1}{2}xy^2, write down the numerical coefficient and the literal coefficient.

(iv) In the term −12xy2-\dfrac{1}{2}xy^2, what is the coefficient of x?

Algebra Basics

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Answer

(i) The given expression 32x2y−12xy2+6x2y2\dfrac{3}{2}x^2y - \dfrac{1}{2}xy^2 + 6x^2y^2 has 3 terms.

Since the expression has three terms, it is called a trinomial.

(ii) The terms of the expression are:

32x2y,−12xy2\dfrac{3}{2}x^2y, -\dfrac{1}{2}xy^2 and 6x2y26x^2y^2

(iii) In the term −12xy2-\dfrac{1}{2}xy^2:

Numerical coefficient = −12-\dfrac{1}{2}

Literal coefficient = xy2

(iv) In the term −12xy2-\dfrac{1}{2}xy^2, the coefficient of x is the remaining factor after removing x from the term.

−12xy2=−12×x×y2-\dfrac{1}{2}xy^2 = -\dfrac{1}{2} \times x \times y^2

Hence, the coefficient of x is −12y2-\dfrac{1}{2}y^2.

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