1. Factorize each of the following expressions: (i) \( 4x^4 + 81y^4 \) \[(2x^2)^2 + (9y^2)^2 + 2(2x^2)(9y^2) – 2(2x^2)(9y^2)\] \[(2x^2 + 9y^2)^2 – 36x^2y^2\] \[(2x^2 + 9y^2)^2 – (6xy)^2\] \[(2x^2 + 9y^2 + 6xy)(2x^2 + 9y^2 – 6xy)\] (ii) \( a^4 + 64b^4 \) \[(a^2)^2 + (8b^2)^2 + 2(a^2)(8b^2) – 2(a^2)(8b^2)\] \[(a^2 + 8b^2)^2…
1. Without using a calculator, evaluate the following: (i) \(\log_2 18 – \log_2 9\) Using the logarithmic property: \(\log_b x – \log_b y = \log_b \frac{x}{y}\): \[\log_2 18 – \log_2 9 = \log_2 \frac{18}{9} = \log_2 2 = 1\] Answer: \(1\) (ii) \(\log_2 64 + \log_2 2\) Using the logarithmic property: \(\log_b x + \log_b…
Explore the complete solution of Exercise 1.3 from the new Math 9th syllabus designed by the Punjab Curriculum and Textbook Board (PCTB), Lahore. This detailed guide simplifies the latest 9th class math concepts to help students excel in their studies 1. The sum of three consecutive integers is forty-two. Find the three integers. Let the…
Discover the fundamentals of real numbers with the latest Class 9 Mathematics syllabus by Punjab Curriculum and Textbook Board (PCTB), Lahore. This comprehensive guide to Exercise 1.1 offers an easy-to-follow introduction for students and educators alike. A real number is any number that can be represented on a number line. This includes both rational and…
