FORM 3 UNIT 1
Lesson 1: Evaluating Algebraic Expressions
1 Quiz
Unit 1 Lesson 1: Exercise 1
Lesson 2: Evaluating more complex Algebraic Expressions
3 Quizzes
Unit 1 Lesson 2: Exercise 1
Unit 1 Lesson 2: Exercise 2
Unit 1 Lesson 2: Exercise 3
Lesson 3: Evaluating Algebraic Fractions
1 Quiz
Unit 1 Lesson 3: Exercise 1
Lesson 4: Addition and subtraction of algebraic terms
3 Quizzes
Unit 1 Lesson 4: Exercise 1
Unit 1 Lesson 4: Exercise 2
Unit 1 Lesson 4: Exercise 3
Lesson 5: Expanding Brackets
3 Quizzes
Unit 1 Lesson 5: Exercise 1
Unit 1 Lesson 5: Exercise 2
Unit 1 Lesson 5: Exercise 3
Lesson 6: Expanding and Simplifying
2 Quizzes
Unit 1 Lesson 6: Exercise 1
Unit 1 Lesson 6: Exercise 2
Lesson 7: Expanding Products of Algebraic Expressions (Binomial Expansion)
5 Quizzes
Unit 1 Lesson 7: Exercise 1
Unit 1 Lesson 7: Exercise 2
Unit 1 Lesson 7: Exercise 3
Unit 1 Lesson 7: Exercise 4
Unit 1 lesson 7: Exercise 5
Lesson 8: Division of algebraic terms
2 Quizzes
Unit 1 Lesson 8: Exercise 1
Unit 1 Lesson 8: Exercise 2
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Lesson 7: Expanding Products of Algebraic Expressions (Binomial Expansion)
FORM 3 UNIT 1
Lesson 7: Expanding Products of Algebraic Expressions (Binomial Expansion)
Objective
At the end of this lesson, students should be able to:
Expand products of algebraic expressions and simplify them.
When multiplying together expressions in brackets, it is necessary to multiply all terms in one bracket by all the terms in the other bracket.
The total area is (a +b) × (c +d)
= (a + b) (c + d)
It is made up of 4 smaller rectangles with areas
ac
,
ad
,
bc
and
bd
So (a + b) (c + d) =
ac
+
ad
+
bc
+
bd
OR
Example 1
Expand and simplify (x + 2) (x + 4).
Solution
All terms in one bracket must be multiplied by each term in the other bracket.
1
^{st}
(
B
1) × 1
^{st}
(
B
2) =
x
^{2}
1
^{st}
(
B
1) × 2
^{nd}
(
B
2) =
4x
2
^{nd}
(
B
1) × 1
^{st}
(
B
2) =
2x
2
^{nd}
(
B
1) × 2
^{nd}
(
B
2) =
8
Example 2
Expand and simplify 2 (6p + 7q) – 3 (2p – 5q)
Solution
2 (6p + 7q) – 3 (2p – 5q)
Collect like terms and simplify
= 12p + 14q – 6p + 15q
= 12p – 6p +14q + 15q
=
6p + 29q
Example 3
Expand and simplify (3x – 3y)
^{2}
Solution
The bracket is squared, so we have to write out the bracket twice and multiply each term.
(3x – 3y)
^{2}
= (3x – 3y)(3x – 3y)
3x(3x) – 3x(3y) – 3y(3x) – 3y(-3y)
9x
^{2}
– 9xy – 9xy + 9y
^{2}
9x
^{2}
– 18xy + 9y
^{2}
Example 4
Simplify (x + 2)(x + 3)
Solution
We multiply x by (x + 3) and 2 by (x + 3)
(x + 2)(x + 3)= x(x + 3) +2 (x + 3)
= x
^{2}
+ 3x + 2x + 6
=
x
^{2}
+ 5x + 6
Example 5
Simplify (x + 4)(x + 3) – x
^{2}
Solution
(x + 4)(x + 3) – x
^{2}
= x(x + 3) + 4(x + 3) – x
^{2}
= x . x + x . 3 + 4. x + 4. 3 – x²
= x
^{2}
+ 3x + 4x + 12- x
^{2}
= (x
^{2}
– x
^{2}
)+ (3x + 4x) + 12
=
7x + 12
Example 6
Simplify (y – 2)(2x + 5)
Solution
(y – 2)(2x + 5) = y(2x + 5)- 2(2x + 5)
=
2xy + 5y – 4x -10.
Lesson Content
Unit 1 Lesson 7: Exercise 1
Unit 1 Lesson 7: Exercise 2
Unit 1 Lesson 7: Exercise 3
Unit 1 Lesson 7: Exercise 4
Unit 1 lesson 7: Exercise 5
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