Identify the monomials, binomials and trinomials in the following:
(i) $ 2 x+y-z $
(ii) $ -2 x^{3} $
(iii) $ -7-p $
(iv) $ 5 x y z $
(v) $ 5-3 y-y^{2} $
(vi) $ m^{2}-1 $
To do:
We have to find the monomials, binomials and trinomials from among the given polynomials.
Solution:
Monomials: Polynomials having only one term are known as monomials.
Binomials: A binomial is a polynomial that is the sum of two terms.
Trinomial: A trinomial is a polynomial consisting of three terms.
(i) \( 2 x+y-z \) contains three terms($2x, y, -z$). Therefore, it is a trinomial.
(ii) \( -2 x^{3} \) contains one term($-2x^3$). Therefore, it is a monomial.
(iii) \( -7-p \) contains two terms($-7, -p$). Therefore, it is a binomial.
(iv) \( 5 x y z \) contains one term($5xyz$). Therefore, it is a monomial.
(v) \( 5-3 y-y^{2} \) contains three terms($5, -3y, -y^2$). Therefore, it is a trinomial.
(vi) \( m^{2}-1 \) contains two terms($m^2, -1$). Therefore, it is a binomial.
Related Articles
- Subtract $3 x y+5 y z-7 z x$ from $5 x y-2 y z-2 z x+10 x y z$.
- Expand each of the following, using suitable identities:(i) \( (x+2 y+4 z)^{2} \)(ii) \( (2 x-y+z)^{2} \)(iii) \( (-2 x+3 y+2 z)^{2} \)(iv) \( (3 a-7 b-c)^{2} \)(v) \( (-2 x+5 y-3 z)^{2} \)(vi) \( \left[\frac{1}{4} a-\frac{1}{2} b+1\right]^{2} \)
- Verify that \( x^{3}+y^{3}+z^{3}-3 x y z=\frac{1}{2}(x+y+z)\left[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}\right] \)
- Verify associativity of addition of rational numbers i.e., $(x + y) + z = x + (y + z)$, when:(i) \( x=\frac{1}{2}, y=\frac{2}{3}, z=-\frac{1}{5} \)(ii) \( x=\frac{-2}{5}, y=\frac{4}{3}, z=\frac{-7}{10} \)(iii) \( x=\frac{-7}{11}, y=\frac{2}{-5}, z=\frac{-3}{22} \)(iv) \( x=-2, y=\frac{3}{5}, z=\frac{-4}{3} \)
- Simplify:$2 x+3 y-4 z-(3 y+5 x-2 z)$
- \Find $(x +y) \div (x - y)$. if,(i) \( x=\frac{2}{3}, y=\frac{3}{2} \)(ii) \( x=\frac{2}{5}, y=\frac{1}{2} \)(iii) \( x=\frac{5}{4}, y=\frac{-1}{3} \)(iv) \( x=\frac{2}{7}, y=\frac{4}{3} \)(v) \( x=\frac{1}{4}, y=\frac{3}{2} \)
- Classify into monomials, binomials and trinomials.$(i)$. $4y-7z$$(ii)$. $y^2$$(iii)$. $x+y-xy$$(iv)$. $100$$(v)$. $ab-a-b$$(vi)$. $5-3t$(viii)$. $4p^2q-4pq^2$ $(viii)$. $7mn$$(ix)$. $z^2-3z+8$$(x)$. $a^2+b^2$$(xi)$. $z^2+z$$(xii)$. $1+x+x^2$
- Find the following products:(i) $(x + 4) (x + 7)$(ii) $(x - 11) (x + 4)$(iii) $(x + 7) (x - 5)$(iv) $(x - 3) (x - 2)$(v) $(y^2 - 4) (y^2 - 3)$(vi) $(x + \frac{4}{3}) (x + \frac{3}{4})$(vii) $(3x + 5) (3x + 11)$(viii) $(2x^2 - 3) (2x^2 + 5)$(ix) $(z^2 + 2) (z^2 - 3)$(x) $(3x - 4y) (2x - 4y)$(xi) $(3x^2 - 4xy) (3x^2 - 3xy)$(xii) $(x + \frac{1}{5}) (x + 5)$(xiii) $(z + \frac{3}{4}) (z + \frac{4}{3})$(xiv) $(x^2 + 4) (x^2 + 9)$(xv) $(y^2 + 12) (y^2 + 6)$(xvi) $(y^2 + \frac{5}{7}) (y^2 - \frac{14}{5})$(xvii) $(p^2 + 16) (p^2 - \frac{1}{4})$
- Factorise:(i) \( x^{3}-2 x^{2}-x+2 \)(ii) \( x^{3}-3 x^{2}-9 x-5 \)(iii) \( x^{3}+13 x^{2}+32 x+20 \)(iv) \( 2 y^{3}+y^{2}-2 y-1 \)
- Subtract:(i) $-5xy$ from $12xy$(ii) $2a^2$ from $-7a^2$(iii) \( 2 a-b \) from \( 3 a-5 b \)(iv) \( 2 x^{3}-4 x^{2}+3 x+5 \) from \( 4 x^{3}+x^{2}+x+6 \)(v) \( \frac{2}{3} y^{3}-\frac{2}{7} y^{2}-5 \) from \( \frac{1}{3} y^{3}+\frac{5}{7} y^{2}+y-2 \)(vi) \( \frac{3}{2} x-\frac{5}{4} y-\frac{7}{2} z \) from \( \frac{2}{3} x+\frac{3}{2} y-\frac{4}{3} z \)(vii) \( x^{2} y-\frac{4}{5} x y^{2}+\frac{4}{3} x y \) from \( \frac{2}{3} x^{2} y+\frac{3}{2} x y^{2}- \) \( \frac{1}{3} x y \)(viii) \( \frac{a b}{7}-\frac{35}{3} b c+\frac{6}{5} a c \) from \( \frac{3}{5} b c-\frac{4}{5} a c \)
- Simplify each of the following expressions:\( (x+y-2 z)^{2}-x^{2}-y^{2}-3 z^{2}+4 x y \)
- Factorise:(i) \( 4 x^{2}+9 y^{2}+16 z^{2}+12 x y-24 y z-16 x z \)(ii) \( 2 x^{2}+y^{2}+8 z^{2}-2 \sqrt{2} x y+4 \sqrt{2} y z-8 x z \)
- If \( 3^{x}=5^{y}=(75)^{z} \), show that \( z=\frac{x y}{2 x+y} \).
- If $x=1,\ y=2$ and $z=5$, find the value of $x^{2}+y^{2}+z^{2}$.
- Express the following linear equations in the form \( a x+b y+c=0 \) and indicate the values of \( a, b \) and \( c \) in each case:(i) \( 2 x+3 y=9.3 \overline{5} \)(ii) \( x-\frac{y}{5}-10=0 \)(iii) \( -2 x+3 y=6 \)(iv) \( x=3 y \)(v) \( 2 x=-5 y \)(vi) \( 3 x+2=0 \)(vii) \( y-2=0 \)(viii) \( 5=2 x \)
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies