Page 83 - Mathematics_F1

Also, (2n + m) × 3 = (2n + m) + (2n + m) + (2n + m)
= (2n + 2n + 2n) + (m + m + m)

= 6n + 3m.
Therefore, (2n + m) × 3 = 6n + 3m.
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The multiplication sign between a number and a bracket is normally dropped
but the meaning remains the same. For example;
3 × (2n + m) = 3(2n + m) = 6n + 3m and 3 × (2n – m) = 3(2n – m) = 6n – 3m.
In general, a(b + c) = ab + ac.
Tanzania Institute of Education
When multiplying an algebraic expression by a number, each term must be
multiplied by the number. Similarly, when dividing an algebraic expression
by a number, each term must be divided by the number.

Example 5.5

Multiply 5a + 2b – 3c by 4.

Solution
(5a + 2b – 3c) × 4 = 4(5a + 2b – 3c)
= 4 × 5a + 4 × 2b + 4 × (–3c)

= 20a + 8b – 12c.
Therefore, 5a + 2b – 3c multiplied by 4 gives 20a + 8b – 12c.

Example 5.6

Multiply 2x – 3y by – 2a.

Solution
Mathematics Form One = (–2a) (2x) + (–2a) (–3y)
(2x – 3y) × (–2a) = (–2a) (2x – 3y)

= – 4ax + 6ay.

Therefore, when 2x – 3y is multiplied by – 2a, the result is – 4ax + 6ay.

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Mathematics form 1.indd 76