This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the factorizations for the given expressions. a) Factorise y^2 - 16y Step 1: Identify the common factor in both terms. Both terms, y^2 and 16y, have y as a common factor. Step 2: Factor out the common factor y. y^2 - 16y = y(y - 16) The completely factorised expression is y(y - 16). b) Factorise 32x^2 - 25 Step 1: Recognize the form as a difference of squares, A^2 - B^2 = (A - B)(A + B). We can write 32x^2 as (sqrt(32)x)^2 and 25 as 5^2. 32x^2 - 25 = (sqrt(32)x)^2 - 5^2 Step 2: Simplify sqrt(32). sqrt(32) = sqrt(16 × 2) = sqrt(16) × sqrt(2) = 4sqrt(2) Step 3: Substitute the simplified radical back into the expression and apply the difference of squares formula. (4sqrt(2)x)^2 - 5^2 = (4sqrt(2)x - 5)(4sqrt(2)x + 5) The completely factorised expression is (4sqrt(2)x - 5)(4sqrt(2)x + 5). c) Factorise 18x^2 - 100x Step 1: Identify the greatest common factor (GCF) of the coefficients and the variables. The coefficients are 18 and 100. The GCF of 18 and 100 is 2. The variables are x^2 and x. The GCF of x^2 and x is x. So, the overall GCF is 2x. Step 2: Factor out the GCF 2x from both terms. 18x^2 - 100x = 2x(9x - 50) The completely factorised expression is 2x(9x - 50). 3 done, 2 left today. You're making progress.