1 of 60 Factorizing Algebraic Expressions
2 of 60 Factorizing expressions Factorizing an expression is the opposite of expanding it. Expanding or multiplying out a(b + c) ab + ac Factorizing Often: When we expand an expression we remove the brackets. When we factorize an expression we write it with brackets.
3 of 60 Factorizing expressions For example, in the expression 5x + 10 the terms 5x and 10 have a common factor, 5 so we can divide each term by 5. 5(x + 2)
4 of 60 Factorizing expressions Writing 5x + 10 as 5(x + 2) is called factorizing the expression. Factorize 6a + 8 Factorize 12 9n The highest common factor of 6a and 8 is 2. (6a + 8) 2 = 3a + 4 6a + 8 = 2(3a + 4) The highest common factor of 12 and 9n is 3. (12 9n) 3 = 4 3n 12 9n = 3(4 3n)
5 of 60 Factorizing expressions Writing 5x + 10 as 5(x + 2) is called factorizing the expression. Factorize 3x + x 2 Factorize 2p + 6p 2 4p 3 The highest common factor of 3x and x 2 is x. (3x + x 2 ) x = 3 + x 3x + x 2 = x(3 + x) The highest common factor of 2p, 6p 2 and 4p 3 is 2p. (2p + 6p 2 4p 3 ) 2p = 1 + 3p 2p 2 2p + 6p 2 4p 3 = 2p(1 + 3p 2p 2 )
6 of 60 Pelmanism: Equivalent expressions
7 of 60 Solving Equations
8 of 60 Equations An equation has 2 sides with an equals sign in the middle. For example, x + 7 = 13 Finding the value of the unknown is called solving the equation. x + 7 = 13 x = 6
9 of 60 Solving equations For example, x + 5 = 13 x = 13 5 x = 8 Always your answers by putting it back into the original equation. If we substitute x = 8 back into x + 5 = 13 we have 8 + 5 = 13
10 of 60 Solving equations Solve the following equations. 5x = 45 17 x = 6 x = 45 5 x = 9 Check: 5 9 = 45 We always write the letter before the equals sign. 17 = 6 + x 17 6 = x 11 = x x = 11 Check: 17 11 = 6
Solving equations Solve the following equations. x 7 = 3 3x 4 = 14 x = 3 7 x = 21 Check: 21 = 3 7 3x = 14 + 4 3x = 18 x = 18 3 x = 6 Check: 3 6 4 = 14 11 of 60
12 of 60 Solving equations Solve this equation: 2x + 5 = 11 Subtract 5 from both sides: 2x = 11 5 2x = 6 Divide both sides by 2: x = 6 2 x = 3
13 of 60 Solving equations Solve this equation: m 4 1 = 2 +1 +1 m 4 = 3 4 4 Add 1 to both sides. Multiply both sides by 4. m = 12 Always check your answer: 12 4 1 = 2
14 of 60 Solving Equations with variables on both sides
15 of 60 Solving the equation Solve this equation 3n 11 = 2n 3 Start by writing the equation down. -2n -2n Subtract 2n from both sides. n 11 = 3 +11 +11 Add 11 to both sides. n = 8 This is the solution. We can check the solution by substituting it back into the original equation: 3 8 11 = 2 8 3
16 of 60 Solving the equation Solve this equation 4n = n + 9 Start by writing the equation down. -n -n Subtract n from both sides. 3n = 9 3 3 Divide both sides by 3. n = 3 This is the solution. We can check the solution by substituting it back into the original equation: 4 3 = 3 + 9
17 of 60 Solving the equation Solve the equation. 2x + 5 = 65 2x +2x +2x Add 2x to both sides. 4x + 5 = 65-5 -5 Subtract 5 from both sides. 4x = 60 4 4 x = 15 Check: Divide both sides by 4. This is the solution. 2 15 + 5 = 65 2 15
18 of 60 Equations with brackets Solve this equation: To solve this we can 2(3x 5) = 4x Multiply out the brackets: 6x 10 = 4x + 10 + 10 Add 10 to both sides: 6x = 4x + 10-4x - 4x Subtract 4x from both sides: 2x = 10 2 2 Divide both sides by 2: x = 5
19 of 60 Substitution
20 of 60 Substitution What does substitution mean? In algebra, when we replace letters in an expression or equation with numbers we call it substitution.
21 of 60 Substitution Evaluate the expression 4 + 3n When n = 5 4 + 3n = 4 + 3 5 = 4 + 15 = 19 When n = 11 4 + 3n = 4 + 3 11 = 4 + 33 = 37
22 of 60 Substitution Evaluate the expression 7n 2 When n = 4 When n = 1.1 7n 2 7n 2 = 7 4 2 = 28 2 = 14 = 7 1.1 2 = 7.7 2 = 3.85
23 of 60 Substitution Evaluate the expression n 2 + 6 When n = 4 n 2 + 6 = 4 2 + 6 = 16 + 6 = 22 When n = 0.6 n 2 + 6 = 0.6 2 + 6 = 0.36 + 6 = 6.36
24 of 60 Substitution Evaluate the expression 2(n + 8) When n = 6 2(n + 8) = 2 (6 + 8) = 2 14 = 28 When n = 13 2(n + 8) = 2 (13 + 8) = 2 21 = 42
25 of 60 Substitution exercise Here are five expressions. 1) a + b + c = 5 + 2 + 1 = 6 2) 3a + 2c 3) a(b + c) = 3 5 + 2 1 = 15 + 2 = 13 = 5 (2 + 1) = 5 1 = 5 4) abc = 5 2 1 = 10 1 = 10 5) b 2 c a = 2 2 1 5 = 5 5 = 1 Evaluate these expressions when a = 5, b = 2 and c = 1.
26 of 60 Noughts and crosses substitution