Question

(X-2)(X-3)(X-4) using standard formula . Expand

Answer 1

We have to expand (x - 2)(x - 3)(x - 4) using standard formula.

Solution : Using standard form, (x - a)(x - b)(x - c) = x³ - (a + b + c)x² + (ab + bc + ca)x - abc

Here, a = 2, b = 3, and c = 4

So, (x - 2)(x - 3)(x - 4) = x³ - (2 + 3 + 4)x² + (2 × 3 + 3 × 4 + 4 × 2)x - 2 × 3 × 4

= x³ - 9x² + 26x - 24

therefore required answer is x³ - 9x² + 26x - 24

another method : we know, from algebraic identities, (x - a)(x - b) = x² - (a + b)x + ab

So, (x - 2)(x - 3) = x² - (2 + 3)x + 2 × 3

= x² - 5x + 6

Now, (x - 2)(x - 3)(x - 4) = (x² - 5x + 6)(x - 4)

= x(x² - 5x + 6) - 4(x² - 5x + 6)

= x³ - 5x² + 6x - 4x² + 20x - 24

= x³ - 9x² + 26x - 24

Answer 2

Answer:

We have to expand (x - 2)(x - 3)(x - 4) using standard formula.

Solution : Using standard form, (x - a)(x - b)(x - c) = x³ - (a + b + c)x² + (ab + bc + ca)x - abc

Here, a = 2, b = 3, and c = 4

So, (x - 2)(x - 3)(x - 4) = x³ - (2 + 3 + 4)x² + (2 × 3 + 3 × 4 + 4 × 2)x - 2 × 3 × 4

= x³ - 9x² + 26x - 24

therefore required answer is x³ - 9x² + 26x - 24

another method : we know, from algebraic identities, (x - a)(x - b) = x² - (a + b)x + ab

So, (x - 2)(x - 3) = x² - (2 + 3)x + 2 × 3

= x² - 5x + 6

Now, (x - 2)(x - 3)(x - 4) = (x² - 5x + 6)(x - 4)

= x(x² - 5x + 6) - 4(x² - 5x + 6)

= x³ - 5x² + 6x - 4x² + 20x - 24

= x³ - 9x² + 26x - 24

Step-by-step explanation: