factorise Completely a) y² − 16y b) 32x² − 25 c) 18x² − 100x

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Here are the factorizations for the given expressions. a) Factorise y² − 16y Step 1: Identify the common factor in both terms. Both terms, y² and 16y, have y as a common factor. Step 2: Factor out the common factor y. y² − 16y = y(y − 16) The completely factorised expression is y(y − 16). b) Factorise 32x² − 25 Step 1: Recognize the form as a difference of squares, A² − B² = (A − B)(A + B). We can write 32x² as (√(32)x)² and 25 as 5². 32x² − 25 = (√(32)x)² − 5² Step 2: Simplify √(32). √(32) = √(16 × 2) = √(16) × √(2) = 4√(2) Step 3: Substitute the simplified radical back into the expression and apply the difference of squares formula. (4√(2)x)² − 5² = (4√(2)x − 5)(4√(2)x + 5) The completely factorised expression is (4√(2)x − 5)(4√(2)x + 5). c) Factorise 18x² − 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 x² and x. The GCF of x² and x is x. So, the overall GCF is 2x. Step 2: Factor out the GCF 2x from both terms. 18x² − 100x = 2x(9x − 50) The completely factorised expression is 2x(9x − 50).

Factorise Completely a) y² - 16y b) 32x² - 25 c) 18x² - 100x

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Step-by-step solution

Part a· 2 steps

Identify the common factor in both terms.

Factor out the common factor $y$ .

Part b· 3 steps
$\mathbf{(4\sqrt{2}x - 5)(4\sqrt{2}x + 5)}$

Recognize the form as a difference of squares, $A^2 - B^2 = (A - B)(A + B)$ .

Simplify $\sqrt{32}$ .

Substitute the simplified radical back into the expression and apply the difference of squares formula.

Part c· 2 steps
$\mathbf{2x(9x - 50)}$

Identify the greatest common factor (GCF) of the coefficients and the variables.

Factor out the GCF $2x$ from both terms.

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