$(i)$ Identify the terms and their factors in the following expressions
Show the terms and factors by tree diagrams.
$(a)$. $x-3$
$(b)$. $1+x+x^2$
$(c)$. $y-y^3$
$(d)$. $5xy^2+7x^2y^7$
$(e)$. $– ab +2b^2-3a^2$
$(ii)$. Identify terms and factors in the expressions given below:
$(a)$. $-4x+5$
$(b)$. $-4x+5y$
$(c)$. $5y +3y^2$
$(d)$. $xy+2x^2y^2$
$(e)$. $pq+q$
$(f)$. $1.2 ab-2.4 b+3.6 a$
$(g)$. $\frac{3}{4}x+\frac{1}{4} $
$(h)$ . $0.1p^2+0.2q^2$
Given: $(i)$. $(a)$. $x-3$ $(b)$. $1+x+x^2$ $(c)$. $y-y^3$
$(d)$. $5xy^2+7x^2y$ $(e)$. $– ab +2b^2-3a^2$
$(ii)$. $(a)$. $-4x+5$ $(b)$. $-4x+5y$ $(c)$. $5y +3y^2$
$(d)$. $xy+2x^2y^2$ $(e)$. $pq+q$ $(f)$. $1.2 ab-2.4 b+3.6 a$
$(g)$. $\frac{3}{4}x+\frac{1}{4}$ $(h)$ . $0.1p^2+0.2q^2$
To do: $(i)$ To identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.
$(ii)$. To identify terms and factors in the expressions given below.
Solution:
$(i)$.
$(a).\ x-3$
Term $=x,\ -3$ and Factor $=x;\ -3$
$(b).\ 1+x+x^2$
Term $= 1,\ x,\ x^2$ and Factor $= 1,\ x,\ (x,\ x)$
$(c).\ y -y^3$
Term $= y,\ -y^3$ and Factor $= y,\ (-1,\ y,\ y,\ y)$
$(d).\ 5xy^2+7x^2y$
Term $= 5xy^2,\ 7x^2y$ and Factor $= (5,\ x,\ y,\ y),\ (7,\ x,\ x,\ y)$
$(e).\ -ab+2b^2 -3a^2$
Term $= -ab,\ 2b^2,\ -3a^2$ and Factor $= (-a,\ b),\ (2,\ b,\ b),\ (-1,\ 3,\ a,\ a)$
$(ii)$.
| S.No. | Expression | Terms | Factors |
| $(a)$ | $-4x+5$
| $-4x,\ 5$ | $-4,\ x,\ 5$ |
$(b)$
| $-4x+5y$
| $-4x,\ 5y$ | $-4,\ x,\ 5,\ 5,\ y$ |
$(c)$
| $5y +3y^2$
| $5y,\ 3y^2$ | $5,\ y,\ 3,\ y,\ y$ |
$(d)$
| $xy+2x^2y^2$
| $xy,\ 2x^2y^2$ | $x,\ y,\ 2,\ x,\ x,\ y,\ y$ |
$(e)$
| $pq+q$
| $pq,\ q$ | $p,\ q,\ q$ |
$(f)$
| $1.2 ab-2.4 b+3.6 a$
| $1.2ab,\ -2.4b,\ 3.6a$ | $1.2,\ a,\ b,\ -2.4,\ b,\ 3.6,\ a$ |
$(g)$
| $\frac{3}{4}x+\frac{1}{4} $
| $\frac{3}{4}x,\ \frac{1}{4}$ | $\frac{3}{4},\ x,\ \frac{1}{4}$ |
$(h)$
| $0.1p^2+0.2q^2$
| $0.1p^2,\ 0.2q^2$ | $0.1,\ p,\ p,\ 0.2,\ q,\ q$ |
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