Factorisation

Answer

Step 1: Find the largest common monomial factor. Largest common factor = 5x Step 2: Divide each term by 5x. 5x^2 ÷ 5x = x -10x ÷ 5x = -2 Step 3: Write the expression in brackets. 5x^2 - 10x = 5x(x - 2…

Answer

Step 1: Find the common factor. Largest common factor = 3xy Step 2: Divide each term by 3xy. 3x^2y ÷ 3xy = x -6xy^2 ÷ 3xy = -2y 9xy ÷ 3xy = 3 Step 3: Write the factorised form. 3x^2y - 6xy^2 + 9xy = 3…

Answer

Step 1: Find the largest common factor by inspection. Common factor = -5a^4x^2 Step 2: Divide each term by -5a^4x^2. -10a^4x^2 ÷ -5a^4x^2 = 2 -15a^6x^4 ÷ -5a^4x^2 = 3a^2x^2 20a^7x^5 ÷ -5a^4x^2 = -4a^3…

Answer

Step 1: Notice the common bracket. Common factor = (a + b) Step 2: Take it outside. 2x(a + b) - 3y(a + b) = (a + b)(2x - 3y) Step 3: Check by multiplying back. (a + b)(2x - 3y) gives 2x(a + b) - 3y(a …

Answer

Step 1: Group the terms. (ax - bx) + (ay - by) Step 2: Take out common factors from each group. x(a - b) + y(a - b) Step 3: Take out the common bracket. (a - b)(x + y) Answer: (a - b)(x + y) Alternati…

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Step 1: Arrange into useful groups. (y^3 - 3y^2) + (2y - 6) - (xy - 3x) Step 2: Take common factors from each group. y^2(y - 3) + 2(y - 3) - x(y - 3) Step 3: Take out the common factor. (y - 3)(y^2 + …

Answer

Step 1: Remove the bracket. a^2 - (b + 5)a + 5b = a^2 - ab - 5a + 5b Step 2: Group terms. (a^2 - ab) - (5a - 5b) Step 3: Take common factors. a(a - b) - 5(a - b) Step 4: Take out the common bracket. (…

Answer

Factorisation works because a common factor is shared by every term, so it can be written outside brackets. Example: 5x^2 - 10x = 5x(x - 2) Check by expanding: 5x(x - 2) = 5x^2 - 10x Answer: Taking ou…