$(i)$ Identify the terms and their factors in the following expressionsShow 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)$ . $0.1p^2+0.2q^2$

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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 $(a)$ $-4x+5$ $-4x,\ 5$ $-4,\ x,\ 5$ $(b)$ $-4x+5y$ $-4x,\ 5y$ $-4,\ x,\ 5,\ 5,\ y$ $(c)$ $5y +3y^2$ $5y,\ 3y^2$ $5,\ y,\ 3,\ y,\ y$ $(d)$ $xy+2x^2y^2$ $xy,\ 2x^2y^2$ $x,\ y,\ 2,\ x,\ x,\ y,\ y$ $(e)$ $pq+q$ $pq,\ q$ $p,\ q,\ q$ $(f)$ $1.2 ab-2.4 b+3.6 a$ $1.2ab,\ -2.4b,\ 3.6a$ $1.2,\ a,\ b,\ -2.4,\ b,\ 3.6,\ a$ $(g)$ $\frac{3}{4}x+\frac{1}{4}$ $\frac{3}{4}x,\ \frac{1}{4}$ $\frac{3}{4},\ x,\ \frac{1}{4}$ $(h)$ $0.1p^2+0.2q^2$ $0.1p^2,\ 0.2q^2$ $0.1,\ p,\ p,\ 0.2,\ q,\ q$
Updated on 10-Oct-2022 13:38:09