Terms, variables and coefficients

Build the expression one step at a time. Raju buys boxes of 4 pens. 1 box gives 4 pens, 2 boxes give 8, 3 boxes give 12… so x boxes give 4x. Do the same for y blue boxes of 5 pencils (5y), add the 3 free pens, and Raju has 4x + 5y + 3 things altogether.

The words. In 4x + 5y + 3:

• the terms are the parts joined by + or –: 4x, 5y and 3;
• x and y, which used to be called letter-numbers, are now called variables (their value can vary);
• 4 and 5, the numbers in front, are the coefficients of x and y;
• 3, which never changes, is a constant.

A garden is l m long and w m wide:

• wire fence on the two lengths: 2l × 100 = 200l;
• wooden fence on the two widths: 2w × 80 = 160w;
• seeds over the whole area: 50 × l × w = 50lw.

Total: ₹(200l + 160w + 50lw). Notice 50lw: two variables multiplied together in one term.

A 20 cm wire bent into a rectangle gives length + width = 10 cm. If the length is x, the width is 10 – x, and the area is x(10 – x) = 10x – x².

Examples 1 and 2 use two variables; Example 3 uses only one. From now on the chapter works with expressions in one variable.