Exercise 8.1 (Revised) - Chapter 9 - Algebraic Expressions & Identities - Ncert Solutions class 8 - Maths

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Chapter 8 - Algebraic Expressions & Identities - NCERT Solutions for Class 8 Maths

Ex 8.1 Question 1.

Identify the terms, their coefficients for each of the following expressions:
(i) $5 x y z^2-3 z y$
(ii) $1+x+x^2$
(iii) $4 x^2 y^2-4 x^2 y^2 z^2+z^2$
(iv) $3-p q+q r-p p$
(v) $\frac{x}{2}+\frac{y}{2}-x y$
(vi) $0.3 a-0.6 a b+0.5 b$

Answer.

(i) Terms: $5 x y z^2$ and $-3 z y$
Coefficient in $5 x y z^2$ is 5 and in $-3 z y$ is -3 .
(ii) Terms: $1=x$ and $x^2$.

Coefficient of $x$ and of $x^2$ is 1 .
(iii) Terms: $4 x^2 y^2=-4 x^2 y^2 z^2$ and $z^2$.

Coefficient in $4 x^2 y^2$ is 4 , coefficient of $-4 x^2 y^2 z^2$ is -4 and coefficient of $z^2$ is 1 .
(iv) Terms: $3,-p q, q r$ and $-r p$

Coefficient of $-p q$ is -1 , coefficient of $q r$ is 1 and coefficient of $-r p$ is -1 .
(v) Terms: $\frac{x}{2}=\frac{y}{2}$ and $-x y$

Coefficient of $\frac{x}{2}$ is $\frac{1}{2}$, coefficient of $\frac{y}{2}$ is $\frac{1}{2}$ and coefficient of $-x y$ is -1 .
(vi) Terms: $0.3 a,-0.6 a b$ and $0.5 b$

Coefficient of $0.3 a$ is 0.3 , coefficient of $-0.6 a b$ is -0.6 and coefficient of $0.5 b$ is 0.5 .
Ex 8.1 Question 2.

Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories:
$
\begin{aligned}
& x+y, 1000, x+x^2+x^3+x^4, 7+y+5 x, 2 y-3 y^2, 2 y-3 y^2+4 y^3=5 x-4 y+3 x y, \\
& 4 z-15 z^2, a b+b c+c d+d a, p q r=p^2 q+p q^2, 2 p+2 q
\end{aligned}
$

Answer.

(i) Since $x+y$ contains two terms. Therefore it is binomial.
(ii) Since 1000 contains one terms. Therefore it is monomial.
(iii) Since $x+x^2+x^3+x^4$ contains four terms. Therefore it is a polynomial and it does not fit in above three categories.

(iv) Since $7+y+5 x$ contains three terms. Therefore it is trinomial.
(v) Since $2 y-3 y^2$ contains two terms. Therefore it is binomial.
(vi) Since $2 y-3 y^2+4 y^3$ contains three terms. Therefore it is trinomial.
(vii) Since $5 x-4 y+3 x y$ contains three terms. Therefore it is trinomial.
(viii) Since $4 z-15 z^2$ contains two terms. Therefore it is binomial.
(ix) Since $a b+b c+c d+d a$ contains four terms. Therefore it is a polynomial and it does not fit in above three categories.
(x) Since $p q r$ contains one terms. Therefore it is monomial.
(xi) Since $p^2 q+p q^2$ contains two terms. Therefore it is binomial.
(xii) Since $2 p+2 q$ contains two terms. Therefore it is binomial.

Ex 8.1 Question 3.

Add the following:
(i) $a b-b c, b c-c a=c a-a b$
(ii) $a-b+a b, b-c+b c, c-a+a c$
(iii) $2 p^2 q^2-3 p q+4=5+7 p q-3 p^2 q^2$
(iv) $l^2+m^2=m^2+n^2: n^2+l^2+2 m+2 m n+2 n l$

Answer.

(i) $a b-b c, b c-c a, c a-a b$

(ii) $a-b+a b, b-c+b c, c-a+a c$

Hence the sum if 0 .

Hence the sum is $a b+b c+a c$.
(iii) $2 p^2 q^2-3 p q+4=5+7 p q-3 p^2 q^2$

(iv) $l^2+m^2: m^2+n^2 ; n^2+l^2: 2 l m+2 m n+2 n l$

Hence the sum is
$
2\left(l^2+m^2+n^2+l m+m n+n\right)
$
Ex 8.1 Question 4.

(a) Subtract $4 a-7 a b+3 b+12$ from $12 a-9 a b+5 b-3$.
(b) Subtract $3 x y+5 y z-7 z x$ from $5 x y-2 y z-2 z x+10 x y z$.
(c) Subtract $4 p^2 q-3 p q+5 p q^2-8 p+7 q-10$ from
$
18-3 p-11 q+5 p q-2 p q^2+5 p^2 q \text {. }
$

Answer.

(a)

(b)

(c)