Algebra Play | Class 8 Mathematics Notes

6.5 The Largest Product

This section addresses a problem involving arranging given digits to form numbers that maximize the product in a multiplication expression of the form □□ × □. Using digits 2, 3, and 5, students are guided to systematically list all possible arrangements and compare their products. The method groups products by the multiplier digit and compares pairs where the multiplier is the same. Algebraic expressions are used to expand the products and compare them term by term, revealing that the largest product is obtained when the largest digit is used as the multiplier and the other two digits are arranged in decreasing order to form the multiplicand. This reasoning is generalized using variables p, q, r representing digits in increasing order. The section encourages students to apply this method to other digit sets to find the largest product and understand the underlying algebraic logic.

🧪 Activity: Fill digits 1, 3, 7 and 3, 5, 9 in □□ × □ to make the largest product possible using the algebraic method.

🔗 Connection: Leads to section 6.6 on Decoding Divisibility Tricks by continuing algebraic reasoning with numbers.