Question

Identify the terms, their coefficients for each of the following expressions,
(i)\[5xy{z^2} - 3zy\]
(ii)\[1 + x + {x^2}\]
(iii)\[4{x^2}{y^2} - 4{x^2}{y^2}{z^2} + {z^2}\]
(iv)\[3 - pq + qr - rp\]
(v)\[\dfrac{x}{2} + \dfrac{y}{2} - xy\]
(vi)\[0.3a - 0.6ab + 0.5b\]

Answer 1

Hint: We will first consider the given expression part wise. As we need to find the terms and the coefficients of the terms, we will form a table in which we will make two columns, one of the terms and the other of coefficients of terms. Coefficient of term is the constant number in any term which multiplies the variables.

Complete step-by-step answer:
(i)We will consider the given expression that is \[5xy{z^2} - 3zy\]
We can rewrite the given expression as: \[5xy{z^2} - 3zy = 5xy{z^2} + \left( { - 3zy} \right)\]
Now, we will form a table consisting of two columns, one column shows the terms from the expression and the other column shows the coefficient of the terms.
Thus, we get,

Terms	Coefficients of terms
\[5xy{z^2}\]	\[5\]
\[ - 3zy\]	\[ - 3\]

(ii)We will consider the given expression that is \[1 + x + {x^2}\]
Now, we will form a table consisting of two columns, one column shows the terms from the expression and the other column shows the coefficient of the terms.
Thus, we get,

Terms	Coefficients of terms
\[1\]	\[1\]
\[x\]	\[1\]
\[{x^2}\]	\[1\]

(iii)We will consider the given expression that is \[4{x^2}{y^2} - 4{x^2}{y^2}{z^2} + {z^2}\]
We can rewrite the given expression as: \[4{x^2}{y^2} - 4{x^2}{y^2}{z^2} + {z^2} = 4{x^2}{y^2} + \left( { - 4{x^2}{y^2}{z^2}} \right) + {z^2}\]
Now, we will form a table consisting of two columns, one column shows the terms from the expression and the other column shows the coefficient of the terms.
Thus, we get,

Terms	Coefficients of terms
\[4{x^2}{y^2}\]	\[4\]
\[ - 4{x^2}{y^2}{z^2}\]	\[ - 4\]
\[{z^2}\]	1

(iv)We will consider the given expression that is \[3 - pq + qr - rp\]
We can rewrite the given expression as: \[3 - pq + qr - rp = 3 + \left( { - pq} \right) + qr + \left( { - rp} \right)\]
Now, we will form a table consisting of two columns, one column shows the terms from the expression and the other column shows the coefficient of the terms.
Thus, we get,

Terms	Coefficients of terms
\[3\]	\[3\]
\[ - pq\]	\[ - 1\]
\[qr\]	1
\[ - rp\]	\[ - 1\]

(v)We will consider the given expression that is \[\dfrac{x}{2} + \dfrac{y}{2} - xy\]

We can rewrite the given expression as: \[\dfrac{x}{2} + \dfrac{y}{2} - xy = \dfrac{1}{2}x + \dfrac{1}{2}y + \left( { - xy} \right)\]

Now, we will form a table consisting of two columns, one column shows the terms from the expression and the other column shows the coefficient of the terms.

Thus, we get,

Terms	Coefficients of terms
\[\dfrac{1}{2}x\]	\[\dfrac{1}{2}\]
\[\dfrac{1}{2}y\]	\[\dfrac{1}{2}\]
\[ - xy\]	\[ - 1\]

(vi)We will consider the given expression that is \[0.3a - 0.6ab + 0.5b\]
We can rewrite the given expression as: \[0.3a - 0.6ab + 0.5b = 0.3a + \left( { - 0.6ab} \right) + 0.5b\]
Now, we will form a table consisting of two columns, one column shows the terms from the expression and the other column shows the coefficient of the terms.
Thus, we get,

Terms	Coefficients of terms
\[0.3a\]	\[0.3\]
\[ - 0.6ab\]	\[ - 0.6\]
\[0.5b\]	\[0.5\]

Note: If the sign before any term is negative then make it positive and take the negative sign in the bracket and rewrite the expression carefully. While finding the coefficients of terms do remember to include the negative sign if any. Terms have the variables included in it but coefficients have the constant part of the term only not the variable.