Question

(2-x)(4-x) please answer with explanation

Answer 1

Question:

$(2 - x)(4 - x)$

It also can be written as,

$(x - 2)(x - 4)$

Answer:

$\boxed{{x}^{2} - 6x + 8}$

Step-by-step explanation:

$(x - 2)(x - 4)$

It's of the form, ( Formula )

$(x + a)(x + b) = {x}^{2} + (a + b)x + ab$

Here, a = - 2, b = - 4

Now, substituting

(x - 2)(x - 4)

= x² + ( - 2 - 4)x + ( - 2 × - 4)

= x² - 6x + 8

Proof:

Proving by factorisation method :

${x}^{2} - 6x + 8 = 0$

Product :- 8 = -4 × -2

Sum :- - 6 = -4 + (-2)

${x}^{2} - 2x - 4x + 8 = 0$

$x(x - 2) - 4(x - 2) = 0$

$(x - 2)(x - 4) = 0$

Hence proved.