NCERT Solutions for Class 9th Maths Chapter 4 Think and Reflect — Factorisation Using Algebra Tiles
Book page 79 Updated on2026-09-08
Q1.
Figure out the product of x + 2 and x + 3 using algebra tiles.
Answer
Lay one x-tile and two unit tiles along the top edge, and one x-tile and three unit tiles down the left edge. Fill the rectangle:
One x²-tile, 2 + 3 = 5 x-tiles and a 2 × 3 array of 6 unit tiles form a rectangle of sides x + 2 and x + 3.
1 x²-tile → x²
3 x-tiles to the right of it and 2 below it → 5x
a 2 × 3 block of unit tiles → 6 (x + 2)(x + 3) = x² + 5x + 6
Why the tiles give the answer: the big rectangle is measured two ways. Its dimensions are x + 2 and x + 3, so its area is (x + 2)(x + 3). But it is also the sum of the areas of the pieces, x² + 5x + 6. One region, two descriptions — and they must be equal. That equality is the identity.
Q2.
Lay out algebra tiles for x² + 11x + 30 in such a way that you will see its factors.
Answer
Split 11x so that the unit tiles form a rectangle of area 30. We need a + b = 11 and ab = 30, so a = 5 and b = 6.
The x²-tile with 5 x-tiles beside it, 6 x-tiles below it and a 5 × 6 array of unit tiles. The finished rectangle measures x + 5 by x + 6.