Question

calculate factor 4(x-a)^3-27a^2x​

Answer 1

factors of 4(x - a)³ - 27a²x is (2x + a), (2x + a) and (x - 4a).

it is given that, 4(x - a)³ - 27a²x

we know from algebraic formula,

(a - b)³ = a³ - 3a²b + 3ab² - b³

so, (x - a)³ = x³ - 3x²a + 3xa² - a³

then, 4(x³ - 3x²a + 3xa² - a³) - 27a²x

= 4x³ - 12x²a + 12a²x - 4a³ - 27a²x

= 4x³ - 12x²a - 15a²x - 4a³

= 4x³ + 2x²a - 14x²a - 7a²x - 8a²x - 4a³

= 2x²(2x + a) - 7ax(2x + a) - 4a²(2x + a)

= (2x + a)[2x² - 7ax - 4a² ]

= (2x + a) [2x² + ax - 8ax - 4a² ]

= (2x + a)[x(2x + a) - 4a(2x + a) ]

= (2x + a)(2x + a)(x - 4a)

hence, factors of 4(x - a)³ - 27a²x is (2x + a), (2x + a) and (x - 4a)

also read similar questions : 6x-2/x=1 Solve this quadratic equation by factorisation.

https://brainly.in/question/4372751

If (x + 4) is a factor of x3 + 2x2 + bx + 68, what is the value of b?

https://brainly.in/question/6603881

Answer 2

Answer:

2x + a, 2x + a and x - 4a

Step-by-step explanation:

Given expression,

$4(x-a)^3- 27 a^2x$.

Using (x-y) = x³ - 3x²y + 3xy² - y³,

$4(x^3-3x^2a+3xa^2-a^3)-27a^2x$

$4x^3-12x^2a+12xa^2-4a^3-27a^2x$

$4x^3-12x^2a-15xa^2-4a^3​$

$4x^3 + 2x^2a - 14x^2a - 7a^2x - 8a^2x - 4a^3$

$2x^2(2x + a) - 7ax(2x + a) - 4a^2(2x + a)$

$(2x + a)(2x^2 - 7ax - 4a^2)$

$(2x + a)(2x^2 + ax - 8ax - 4a^2)$

$(2x + a)(x(2x + a) - 4a(2x + a) )$

$(2x + a)(2x + a)(x - 4a)$

Hence, factors are,

2x + a, 2x + a and x - 4a