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Please browse the website by using navigation bar or search the website. Solutions of all the chapters are given below. YouTube Channel International exposure … which are great. See more of MathCity on Facebook. Software Class 9 Mathematics Notes - Chapter 3 - Logarithms - Exercise 3.2. mathcity bsc calculus. This Chapter belongs to 9th Class Mathematics book. Home Welcome to MathCity.org. Participate Create New Account. Class 9 Maths Notes for FBISE - Notes, Solved Exercises Algebra is a division of mathematics designed to help solve certain types of problems quicker and easier. These CBSE Class 9 notes are prepared by referring to CBSE Class 9 syllabus. Class 9 Mathematics Notes - Chapter 9 - Introduction to Coordinate Geometry - Exercise 9.1. Class 9 Mathematics Notes - Chapter 9 - Introduction to Coordinate Geometry - Exercise 9.2. The Vedantu team has verified how many exercises and types of questions are there in Euclid Geometry Class 9. Mathematics Class 9 Unit 2 Real and Complex Numbers Exercise 2.6 Complete Solution Punjab Textbook Board and Federal Board Pakistan Log In. Stage Design - A Discussion between Industry Professionals. Twitter Advertisement. We will keep adding updated notes, past papers, guess papers and other materials with time. BSc Section Mathematics Class 9 Unit 4 Algebraic Expressions and Algebraic Formulas Exercise 4.1 Complete Solution Punjab Textbook Board and Federal Board Pakistan View definition chapter 18 9th class.pdf from ACCOUNTING MISC at Bahauddin Zakaria University, Multan. 11 Feb 2013. Links You Might Be Interested In: Recent Posts. With an aim to make math easy, we at Byju’s are providing a comprehensive set of CBSE Class 9 maths notes which will help students to study effectively as well as score well in the examination. This book consist of 302 pages and there are 17 units. Book . Your email address will not be published. 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(iii) $\frac{1}{16}x^2-\frac{1}{12}xy+ \frac{1}{36}y^2$, (v) $\frac{4x^6-12x^3y^3+9y^6}{9x^4-24x^2y^2+16y^4},(x \neq 0)$, (vi) $\left( x+\frac{1}{x}\right)^2-4\left( x-\frac{1}{x}\right)$, (vii) $\left( x^2+\frac{1}{x^2}\right)^2-4 \left( x+\frac{1}{x}\right)^2+12,(x \neq 0)$, $\begin{align}4x^2-12xy +9y^2\\&=4x^2-6xy-6xy +9y^2\\&= 2x(2x-3y)-3y(2x-3y)\\&= (2x-3y)(2x-3y)\\&= (2x-3y)^2 \end{align}$, $\begin{align} \sqrt{4x^2-12xy +9y^2}&= \pm (2x-3y) \end{align}$, $\begin{align}x^2-1+\frac{1}{4x^2}\\&=(x)^2-1+(\frac{1}{2x})^2\\&=(x)^2-2x(\frac{1}{2x})+(\frac{1}{2x})^2\\&= (x-\frac{1}{2x})^2 \end{align}$, $\begin{align} \sqrt{x^2-1+\frac{1}{4x^2}}&= \pm (x-\frac{1}{2x}) \end{align}$, $\begin{align}\frac{1}{16}x^2-\frac{1}{12}xy+ \frac{1}{36y^2}\\&=(\frac{1}{4}x)^2-\frac{1}{12}xy+ (\frac{1}{6y})^2\\&=(\frac{1}{4}x)^2-2(\frac{1}{4})x(\frac{1}{6y})+ (\frac{1}{6y})^2\\&= (\frac{x}{4}-\frac{1}{6y})^2 \end{align}$, $\begin{align} \sqrt{\frac{1}{16}x^2-\frac{1}{12}xy+ \frac{1}{36}y^2}&= \pm (\frac{x}{4}-\frac{1}{6y}) \end{align}$, $\begin{align}4(a+b)^2-12(a^2-b^2)+9(a-b)^2\\&=[2(a+b)]^2-2(2)(a+b)(3)(a-b)+[3(a-b)]^2\\&=(2(a+b)-3(a-b))^2\\&= (2a+2b-3a+3b)^2 \\&=(5b-a)^2 \end{align}$, $\begin{align} \sqrt{4(a+b)^2-12(a^2-b^2)+9(a-b)^2}&= \pm (5b-a) \end{align}$, (v) $\frac{4x^6-12x^3y^3+9y^6}{9x^4+24x^2y^2+16y^4},(x \neq 0)$, $\begin{align}\frac{4x^6-12x^3y^3+9y^6}{9x^4+24x^2y^2+16y^4}\\&=\frac{(2x^3)^2-2(2x^3)(3y^3)+(3y^3)^2}{(3x^2)^2+2(3x^2)(3y^2)+(4y^2)^2}\\&=\frac{(2x^3-3y^3)^2}{(3x^2+4y^2)^2} \end{align}$, $\begin{align} \sqrt{\frac{4x^6-12x^3y^3+9y^6}{9x^4+24x^2y^2+16y^4}}&= \pm \frac{(2x^3-3y^3)}{(3x^2+4y^2)} \end{align}$, Now $\begin{align}\left(x+\frac{1}{x}\right)^2 &=(x-\frac{1}{x})^2+4\\&= a^2+4 \end{align}$, $\begin{align}\left( x+\frac{1}{x}\right)^2-4\left( x-\frac{1}{x}\right) &=(a^2+4)-4a \\&= a^2-4a+4\\&=(a-2)^2\\&=\left[ (x-\frac{1}{x})-2\right]^2 \end{align}$, $\begin{align} \sqrt{\left( x+\frac{1}{x}\right)^2-4\left( x-\frac{1}{x}\right)}&= \pm \left[ (x-\frac{1}{x})-2\right]\end{align}$, Now $\begin{align}\left(x+\frac{1}{x}\right)^2 &=a^2\end{align}$, $\begin{align}\left(x^2+\frac{1}{x^2}+2\right) &= a^2\end{align}$, $\begin{align}\left(x^2+\frac{1}{x^2}\right) &= a^2-2\end{align}$, $\begin{align}\left( x^2+\frac{1}{x^2}\right)^2-4 \left( x+\frac{1}{x}\right)^2+12 &=(a^2-2)^2-4a^2+12 \\&= a^2-4a+4\\&=a^4-4a^2+4-4a^2+12\\&=(a^2)^2-2(a^2)(4)+(4)^2\\&=(a^2-4)^2\end{align}$, $\begin{align} \sqrt{\left( x^2+\frac{1}{x^2}\right)^2-4 \left( x+\frac{1}{x}\right)^2+12}&= \pm \left[ (a^2-4)\right]\\&= \pm \left[(x+\frac{1}{x})^2-4 \right]\end{align}$, $\begin{align}(x^2+3x+2)(x^2+4x+3)(x^2+5x+6) &= (x^2+2x+x+2)(x^2+x+3x+3)(x^2+2x+3x+6)\\&= (x(x+2)+1(x+2))(x(x+1)+3(x+1))(x(x+2)+3(x+2))\\&= (x+2)(x+1)(x+1)(x+3)(x+2)(x+3)\\&= (x+2)^2(x+1)^2(x+3)^2\end{align}$, $\begin{align} \sqrt{(x^2+3x+2)(x^2+4x+3)(x^2+5x+6)}&= \pm (x+2)(x+1)(x+3)\end{align}$, $\begin{align}(x^2+8x+7)(2x^2-x-3)(2X^2+11x-21)&= (x^2+x+7x+7)(2x^2-3x+2x-3)(2x^2+14x-3x-21)\\&=(x(x+1)+7(x+1))(x(2x-3)+1(2x-3))(2x(x+7)-3(x+7))\\&=(x+1)(x+7)(2x-3)(x+1)(x+7)(2x-3)\\&= (x+1)^2(x+7)^2(2x-3)^2\end{align}$, $\begin{align} \sqrt{(x^2+8x+7)(2x^2-x-3)(2X^2+11x-21)}&= \pm (x+1)^2(x+7)^2(2x-3)^2\end{align}$, Home Bsc solution, past paper for 9th to BSc solution, past paper 9th... 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