Class 9th · Mathematics · Chapter 4
Chapter 4: Factorization and Algebraic Manipulation
Chapter 4 of the Punjab Board Class 9th Mathematics textbook runs from page 67 to 83. Its exercise has exercise, exercise, exercise, exercise and exercise. Open any of those pages in GenZ Books, tap a question, and the answer is worked from this chapter.
Open Chapter 4 of Mathematics in GenZ Books
The same Class 9th textbook, page for page. Tap any question and get the answer worked from that chapter — English and Urdu.
Exercise
- Exercisep. 71
- Exercisep. 75
- Exercisep. 79
- Exercisep. 81
- Exercisep. 82
A sample answer from GenZ Books
Solve · page 83: 4. Find square root by factorization and division method of the expression
Solution This is a general instruction heading for an exercise rather than a single standalone expression. To demonstrate the required methods for finding the square root [جذر مربع], let us take a standard algebraic expression from this chapter, such as $4x^2 + 12x + 9$.
$$\sqrt{4x^2 + 12x + 9}$$
$$(2x)^2 + 2(2x)(3) + (3)^2$$
$$(2x + 3)^2$$
$$\pm (2x + 3)$$
$\pm (2x + 3)$
Explanation
- Grouped the terms into the standard form of a complete square trinomial matching the algebraic identity $a^2 + 2ab + b^2 = (a+b)^2$.
- Rewrote the expression as the square of a binomial using the algebraic identity.
- Took the square root [جذر مربع] of the squared binomial, including the positive and negative signs.
AI-generated from the chapter text by GenZ Books. It can make mistakes — check it against your textbook and your teacher.