J17

3. (2a + b)(c + 3d) 4. (x - y)(4 - z)
5. (a – 3d)(4c - b) 6. (8x + y)(a + 1)
7. (2u - v)(3x - y) 8. (p + q)(s - t)
9. (x + y)(c - 5) 10. (x + 1)(y - 1)
11. (x + 2 1 )(y + 4
1
) 12. (u + w)(a + 2)
13. (5a + 4)(b - 3) 14. (x + y)(
1 a - c)
2
Consider the product of (x + 3)(x + 4).
(x + 3)(x + 4) = x(x + 4) + 3(x + 4)
= x 2 + 4x + 3x + 12
= x 2 + 7x + 12
Quadratic expressions
This kind of an expression where the highest power is 2 is called a quadratic
expression. Most quadratic expressions have three distinct terms known as
the quadratic term (x 2 ), the linear term (7x) and the number term or constant
term (12).
A quadratic expression must have the quadratic term which should also be
the term with the highest power of the unknown letter. For example,
x 2 + 3x + 1, a 2 + 2a, y 2 – 2y + 1, c 2 – 4, e.t.c. but x 3 – 2x, 2x 3 – x 2 + 6, 4x +8
are not.
Example
Expand and simplify:
(a) (2x + 1)(x + 3) (b) (x – 5)(x – 2),
(c) (2a – 3)(5a – 4).
Solutions
(a) (2x + 1)(x + 3) = 2x(x + 3) + 1(x + 3)
= 2x 2 + 6x + x + 3
= 2x 2 + 7x + 3
(b) (x – 5)(x – 2) = x(x – 2) – 5(x – 2)
= x 2 – 2x – 5x + 10
= x 2 – 7x + 10
(c) (2a - 3)(5a – 4) = 2a(5a – 4) – 3(5a – 4)
= 10a 2 – 8a – 15a + 12
= 10a 2 – 23a + 12
Exercise
Expand and simplify.