Algebraic Expressions and Identities - Class 8 - Mathematics
Renews every month. Cancel anytime
Your personal doubt-solving assistant
Chatterbot AI gives you 100% accurate answers to your questions in an instant.
Examples - Algebraic Expressions and Identities | NCERT | Mathematics | Class 8
Add: $7 x y+5 y z-3 z x, 4 y z+9 z x-4 y,-3 x z+5 x-2 x y$
To add the given polynomials, $7xy + 5yz - 3zx, 4yz + 9zx - 4y, -3xz + 5x - 2xy$, follow these steps:
Identify like terms: Like terms are those that contain the same variables raised to the same power. In this context, terms involving $xy$, $yz$, $zx$ (or equivalently $xz$), and single variable terms $x$ and $y$ can be combined.
Combine like terms:
For $xy$: Combine $7xy$ and $-2xy$ to get $5xy$.
For $yz$: Combine $5yz$ and $4yz$ to get $9yz$.
For $zx$ (same as $xz$): Combine $-3zx$, $9zx$, and $-3xz$ to get $3zx$.
For $x$: You only have $5x$, so it remains as it is.
For $y$: You only have $-4y$, so it remains as it is.
Sum up the results: Finally, sum up the combined like terms to get the total sum: $$5xy + 9yz + 3zx + 5x - 4y$$
So, the sum of $7xy + 5yz - 3zx$, $4yz + 9zx - 4y$, and $-3xz + 5x - 2xy$ is $5xy + 9yz + 3zx + 5x - 4y$.
Subtract $5 x^{2}-4 y^{2}+6 y-3$ from $7 x^{2}-4 x y+8 y^{2}+5 x-3 y$.
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowExercise 8.1 - Algebraic Expressions and Identities | NCERT | Mathematics | Class 8
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) $l^{2}+m^{2}, m^{2}+n^{2}, n^{2}+l^{2}$
$2 l m+2 m n+2 n l$
The results of the column-wise additions are:
(i) $0$
(ii) $ab + ac + b*c$
(iii) $9 + 4pq - p^2*q^2$
(iv) $2l^2 + 2lm + 2m^2 + 2ln + 2mn + 2*n^2$
Subtract $4 a-7 a b+3 b+12$ from $12 a-9 a b+5 b-3$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowSubtract $3 x y+5 y z-7 z x$ from $5 x y-2 y z-2 z x+10 x y z$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowSubtract $4 p^{2} q-3 p q+5 p q^{2}-8 p+7 q-10$ from $18-3 p-11 q+5 p q-2 p q^{2}+5 p^{2} q$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowExercise 8.2 - Algebraic Expressions and Identities | NCERT | Mathematics | Class 8
Find the product of the following pairs of monomials.
(i) $4,7 p$
(ii) $-4 p, 7 p$
(iii) $-4 p, 7 p q$
(iv) $4 p^{3},-3 p$
(v) $4 p, 0$
The products of the given pairs of monomials are:
(i) $28p$
(ii) $-28p^2$
(iii) $-28p^2q$ (Simplifying $-28 * p * pq$ gives $-28p^2q$)
(iv) $-12p^4$
(v) $0$
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.
$(p, q) ;(10 m, 5 n) ;\left(20 x^{2}, 5 y^{2}\right) ;\left(4 x, 3 x^{2}\right) ;(3 m n, 4 n p)$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowComplete the table of products.
$\frac{\text{First monomial} \rightarrow}{\text{Second monomial} \downarrow}$ | $2x$ | $-5y$ | $3x^2$ | $-4xy$ | $7x^2y$ | $-9x^2y^2$ |
---|---|---|---|---|---|---|
$2x$ | $4x^2$ | |||||
$-5y$ | ||||||
2$ | $-15x^2y$ | |||||
4xy$ | ||||||
$7x^2y$ | ||||||
$-9 x^{2} y^{2}$ |
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowObtain the volume of rectangular boxes with the following length, breadth and height respectively.
(i) $5 a, 3 a^{2}, 7 a^{4}$
(ii) $2 p, 4 q, 8 r$
(iii) $x y, 2 x^{2} y, 2 x y^{2}$
(iv) $a, 2 b, 3 c$.
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowObtain the product of
(i) $x y, y z, z x$
(ii) $a,-a^{2}, a^{3}$
(iii) $2,4 y, 8 y^{2}, 16 y^{3}$
(iv) $a, 2 b, 3 c, 6 a b c$
(v) $m,-m n, m n p$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowExercise 8.3 - Algebraic Expressions and Identities | NCERT | Mathematics | Class 8
Carry out the multiplication of the expressions in each of the following pairs.
(i) $4 p, q+r$
(ii) $a b, a-b$
(iii) $a+b, 7 a^{2} b^{2}$
(iv) $a^{2}-9,4 a$
(v) $p q+q r+r p, 0$
Here are the results of carrying out the multiplication of the expressions in each of the given pairs:
$(i) , 4p \times (q+r) = 4pq + 4pr$
$(ii) , ab \times (a-b) = a^2b - ab^2$
$(iii) , (a+b) \times 7a^2b^2 = 7a^3b^2 + 7a^2b^3$
$(iv) , (a^2-9) \times 4a = -36a + 4a^3$
$(v) , (pq+qr+rp) \times 0 = 0$
Complete the table.
First expression | Second expression | Product | |
---|---|---|---|
(i) | $a$ | $b+c+d$ | |
(ii) | $x+y-5$ | $5 x y$ | |
(iii) | $p$ | $6 p^{2}-7 p+5$ | |
(iv) | $4 p^{2} q^{2}$ | $p^{2}-q^{2}$ | |
(v) | $a+b+c$ | $a b c$ |
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowFind the product.
(i) $\left(a^{2}\right) \times\left(2 a^{22}\right) \times\left(4 a^{26}\right)$
(ii) $\left(\frac{2}{3} x y\right) \times\left(\frac{-9}{10} x^{2} y^{2}\right)$
(iii) $\left(-\frac{10}{3} p q^{3}\right) \times\left(\frac{6}{5} p^{3} q\right)$
(iv) $x \times x^{2} \times x^{3} \times x^{4}$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up now(a) Simplify $3 x(4 x-5)+3$ and find its values for
(i) $x=3$
(ii) $x=\frac{1}{2}$.
(b) Simplify $a\left(a^{2}+a+1\right)+5$ and find its value for
(i) $a=0$
(ii) $a=1$
(iii) $a=-1$.
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up now(a) Add: $p(p-q), q(q-r)$ and $r(r-p)$
(b) Add: $2 x(z-x-y)$ and $2 y(z-y-x)$
(c) Subtract: $3 l(l-4 m+5 n)$ from $4 l(10 n-3 m+2 l)$
(d) Subtract: $3 a(a+b+c)-2 b(a-b+c)$ from $4 c(-a+b+c)$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowExtra Questions - Algebraic Expressions and Identities | NCERT | Mathematics | Class 8
Evaluate:
$$ (4pq + 3q)^2 - (4pq - 3q)^2 $$
(A) $48pq^2$
(B) $48p^2q$
(C) $48p^2q^2$
(D) $48pq$
The correct option is (A) $48pq^2$
We start by recognizing the given expression as a difference of squares. The expression can be written as: $$ (4pq + 3q)^2 - (4pq - 3q)^2 $$ This can be simplified using the identity for the difference of squares, which is: $$ (a^2 - b^2) = (a+b)(a-b) $$ Here, let $a = 4pq + 3q$ and $b = 4pq - 3q$.
Applying the identity: $$ [(4pq + 3q) - (4pq - 3q)] [(4pq + 3q) + (4pq - 3q)] $$ Simplifying inside the brackets: $$ [4pq + 3q - 4pq + 3q][4pq + 3q + 4pq - 3q] $$ This reduces to: $$ [6q][8pq] $$ Thus, multiplying these, we get: $$ 48pq^2 $$
Therefore, the correct answer is indeed $(A)$ $48pq^2$.
Divide $x^{4a} + x^{2a}y^{2b} + y^{4b}$ by $x^{2a} + x^{a}y^{b} + y^{2b}$
Improve your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up nowImprove your grades!
Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.
Sign up now