Chapter 8 Algebraic Expressions and Identities Ex 8.3 NCERT Solutions for Class 8 Maths

Latest Updated : November 2023

If you are in search of NCERT solutions for Class 8 Maths Chapter 8 Algebraic Expressions and Identities, then you are at the right place. When it comes to Mathematics, it is a subject that holds value for students across various academic streams, be it science, biology, or commerce and having a very good understanding of basic math concepts will help you in achieving your goal and make it much more easier.

Here we provide detailed NCERT solutions for Class 8 Maths of all the chapters, exercise wise with updated syllabus by NCERT. These NCERT solutions for Class 8 Maths have been carefully crafted to provide detailed explanations, ensuring that students can grasp the concepts effectively. We also provide extra practice questions for the same, so feel free to bookmark ncertforclass8.com to boost your preparation.

NCERT Solutions for Class 8 Maths Chapter 8 Algebraic Expressions and Identities Ex 8.3

NCERT Solutions for Class 8 Maths Chapter 8 Algebraic Expressions and Identities Ex 8.3

Class 8 Maths Chapter 8 Algebraic Expressions and Identities Exercise 8.3

Exercise 8.3

1. Carry out the multiplication of the expressions in each of the following pairs.

\[(i)\ 4p\ ,\ q+r\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (ii)\ ab,\ a-b\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (iii)\ a+b,\ 7a^2b^2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (iv)\ a^2-9\ ,\ 4a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (v)\ pq+qr+rp,\ 0\]

Solution :

\[(i)\ 4p(q+r)=4pq+4pr\]

\[(ii)\ ab(a-b)=a^2b-ab^2\]

\[(iii)\ (a+b)\ (7a^2b^2\ )=7a^3b^2+7a^2b^3\]

\[(iv)\ (a^2-9)(4a)=4a^3-36a\]

\[(v)\ (pq+qr+rp)\times0=0\]

2. Complete the table.

Solution:

3. Find the product.

\[\left(i\right)\ \left(a^2\right)\ \times\ \left(2a^{22}\right)\ \times\ \left(4a^{26}\right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(ii\right)\ \left(\frac{2}{3}xy\right)\ \times\ \left(-\frac{9}{10}x^2y^2\right)\]

\[\left(iii\right)\ \left(-\frac{10}{3}pq^3\right)\ \times\ \left(\frac{6}{5}p^3q\right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left(iv\right)\ x\ \times\ x^2\ \times\ x^3\ \times\ x^4\]

Solution :

\[\left(i\right)\ \left(a^2\right)\ \times\ \left(2a^{22}\right)\ \times\ \left(4a^{26}\right)\]

\[=(2\times4)\ \times(a^2\times a^{22}\times a^{26})\]

\[=8\times\left(a^{2+22+26}\right)\]

\[=8a^{50}\]

\[\ \left(ii\right)\ \left(\frac{2}{3}xy\right)\ \times\ \left(-\frac{9}{10}x^2y^2\right)\]

\[=\left(\ \frac{2}{3}\times-\frac{9}{10})\right)\times\ (x\times x^2\times y\times y^2)\]

\[=(-\frac{3}{5}x^3y^3)\]

\[\left(iii\right)\ \left(-\frac{10}{3}pq^3\right)\ \times\ \left(\frac{6}{5}p^3q\right)\]

\[=(-\frac{10}{3}\times\frac{6}{5})\times(p\times p^3\times q^3\times q)\]

\[=(-4p^4q^4)\]

\[\left(iv\right)\ x\ \times\ x^2\ \times\ x^3\ \times\ x^4\]

\[=x^{1+2+3+4}\]

\[=x^{10}\]

4. (a) Simplify 3x (4x – 5) + 3 and find its values for
(i) x = 3 (ii) x =1/2

Solution :

\[a)\ 3x\ (4x-5)+3\]

\[=3x\ (4x)-3x\ (5)+3\]

\[=12x^2-15x+3\]

\[(i)Putting\ x=3\ \ in\ the\ equation\ \ 12x^2-15x+3\ we\ get\]

\[=12(32)-15(3)+3\]

\[=108\ -\ 45\ +\ 3\ =\ 66\]

\[(ii)Putting\ x=\frac{1}{2}\ \ in\ the\ equation\ 12x^2-15x+3\ we\ get\]

\[=12\left(\frac{1}{2}\right)^2-15\left(\frac{1}{2}\right)+3\]

\[=12\left(\frac{1}{4}\right)-\frac{15}{2}+3\]

\[=3-\frac{15}{2}+3\]

\[=6-\frac{15}{2}=\ \frac{\left(12-15\right)}{2}\]

\[=-3/2\]

\[\left(b\right)\ Simplify\ a\left(a^2\ +\ a\ +\ 1\right)\ +5\ and\ find\ its\ values\ for\ \ \left(i\right)\ a=0\ \ ,\ \ \ \left(ii\right)\ a\ =1,\ \ \left(iii\right)\ a\ =\ -1\]

Solution:

\[=a\times a^2+a\times a+a\times1+5\]

\[=a^3+a^2+a+5\]

\[(i)\ putting\ a=0\ in\ the\ equation\ we\ get\ =\ 0^3+0^2+0+5=\ 5\]

\[(ii)\ putting\ a=1\ in\ the\ equation\ we\ get\ =1^3+1^2+1+5=1+1+1+5=8\]

\[(iii)\ Putting\ a=-1\ in\ the\ equation\ we\ get\ =(-1)^3+(-1)^2+(-1)+5=-1+1-1+5=4\]

5. (a) Add: p ( p – q), q ( q – r) and r ( r – p)

Solution :

\[a)\ p(p-q)+q(q-r)+r(r-p)\]

\[=(p^2-pq)+(q^2-qr)+(r^2-pr)\]

\[=p^2+q^2+r^2-pq-qr-pr\]

(b) Add: 2x (z – x – y) and 2y (z – y – x)

Solution :

\[b)\ 2x\ (z-x-y)+2y\ (z-y-x)\]

\[=(2xz-2x^2-2xy)+(2yz-2y^2-2xy)\]

\[=2xz-4xy+2yz-2x^2-2y^2\]

(c) Subtract: 3l (l – 4 m + 5 n) from 4l ( 10 n – 3 m + 2 l )

Solution :

\[c)\ 4l\ (10n-3m+2l)-3l(l-4m+5n)\]

\[=(40\ln-12lm+8l^2)-(3l^2-12lm+15\ln)\]

\[=40\ln-12lm+8l^2-3l^2+12lm-15\ln\]

\[=25\ln+5l^2\]

(d) Subtract: 3a (a + b + c ) – 2 b (a – b + c) from 4c ( – a + b + c )

Solution :

\[d)\ 4c\ (-a+b+c)-3a\ (a+b+c)-2b(a-b+c)\]

\[=(-4ac+4bc+4c^2)-(3a^2+3ab+3ac-(2ab-2b^2+2bc))\]

\[=-4ac+4bc+4c^2-(3a^2+3ab+3ac-2ab+2b^2-2bc)\]

\[=-4ac+4bc+4c^2-3a^2-3ab-3ac+2ab-2b^2+2bc\]

\[=-7ac+6bc+4c^2-3a^2-ab-2b^2\]

Using Class 8 NCERT solutions offers several key advantages for students:

  1. Accurate Answers: NCERT solutions for Class 8 Maths are prepared by expert educators and thoroughly reviewed to ensure quality and accurate answers.
  2. Aligned with Curriculum: NCERT Solutions for Class 8 Maths are specifically designed to go along with the CBSE curriculum, making them the ideal resource for students studying in CBSE affiliated schools.
  3. Crisp an Clear Explanation: The NCERT solutions for Class 8 Maths provide step by step explanations, making complex concepts easier to understand. This helps students to grasp the concepts easily and build a better foundation.
  4. Time-Saver: Instead of spending extra time searching for answers, students can quickly access these NCERT solutions for Class 8 Maths , saving time and allowing them to focus on other aspects of their studies.
  5. Extra Questions: NCERT Solutions for Class 8 Maths also has extra questions that offer additional opportunities for students to build better problem solving skills.
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Summary

On our platform ncertforclass8.com, you will get all the NCERT Solutions for Class 8 Maths expertly solved, ensuring utmost care and accuracy. The NCERT book for Class 8 Maths is strictly followed while creating the NCERT solutions for Class 8 Maths, adhering to the latest CBSE guidelines. We make sure to provide you quality content which will help you to understand the concepts in the best way possible. Also our solutions are completely free for you to access. You have the freedom to copy the NCERT Solutions for Class 8 Maths, download them and even create PDF’s, making it convenient for your offline use.

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