Algebraic ManipulationEdexcel GCSE Maths: Flashcards
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What does 'collecting like terms' mean in algebra?
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- What does 'collecting like terms' mean in algebra?
- Combining terms that have the same variable(s) raised to the same power. For example, 3x + 5x = 8x. Only the coefficients are added or subtracted; the variable part remains unchanged.
- Simplify: 4a + 7b - 2a + 3b
- 2a + 10b. Collect the 'a' terms: 4a - 2a = 2a. Collect the 'b' terms: 7b + 3b = 10b.
- Expand the single bracket: 3(2x + 5)
- 6x + 15. Multiply each term inside the bracket by 3: (3 × 2x) + (3 × 5).
- Expand the double brackets: (x + 2)(x + 3)
- x² + 5x + 6. Use FOIL: First (x × x = x²), Outer (x × 3 = 3x), Inner (2 × x = 2x), Last (2 × 3 = 6). Simplify: x² + 5x + 6.
- Expand the triple brackets: (x + 1)(x + 2)(x + 3)
- x³ + 6x² + 11x + 6. First expand two brackets: (x + 1)(x + 2) = x² + 3x + 2. Then multiply by the third: (x² + 3x + 2)(x + 3) = x³ + 6x² + 11x + 6.
- What does factorising an expression mean?
- Writing an expression as a product of its factors. It is the reverse of expanding brackets. For example, 6x + 9 = 3(2x + 3).
- Factorise by taking out the common factor: 8a² + 12a
- 4a(2a + 3). The highest common factor of 8a² and 12a is 4a. Divide each term by 4a and place it outside the bracket.
- Factorise the difference of two squares: x² - 16
- (x + 4)(x - 4). The difference of two squares follows the pattern a² - b² = (a + b)(a - b). Here, x² - 4² = (x + 4)(x - 4).
- Factorise the quadratic expression: x² + 7x + 12
- (x + 3)(x + 4). Find two numbers that multiply to give 12 and add to give 7: these are 3 and 4. The factorisation is (x + 3)(x + 4).
- Factorise the quadratic expression: 2x² + 7x + 3 (HT)
- (2x + 1)(x + 3). For ax² + bx + c, find two numbers that multiply to ac (2 × 3 = 6) and add to b (7): these are 6 and 1. Rewrite: 2x² + 6x + x + 3, then factorise by grouping: 2x(x + 3) + 1(x + 3) = (2x + 1)(x + 3).
- Simplify the algebraic fraction by factorising and cancelling: (x² + 5x)/(x + 5) (HT)
- x. Factorise the numerator: x(x + 5). Cancel the common factor (x + 5): x(x + 5)/(x + 5) = x.
- Add the algebraic fractions: 3/x + 2/x (HT)
- 5/x. Since the denominators are the same, add the numerators: (3 + 2)/x = 5/x.
- Subtract the algebraic fractions: 4/(x+1) - 2/(x+1) (HT)
- 2/(x+1). Since the denominators are the same, subtract the numerators: (4 - 2)/(x+1) = 2/(x+1).
- Multiply the algebraic fractions: (2/x) × (3/4) (HT)
- 6/(4x) = 3/(2x). Multiply numerators together and denominators together: (2 × 3)/(x × 4) = 6/(4x), then simplify by cancelling the common factor 2.
- Divide the algebraic fractions: (5/x) ÷ (2/3) (HT)
- 15/(2x). To divide by a fraction, multiply by its reciprocal: (5/x) × (3/2) = 15/(2x).