Y=(x-1)(x-4)^2 please help?

Question

can i have a step by step to the simplest function???

Answer 1

Given function is y = (x - 1)(x - 4)²

Apply (a - b)² = a² + b² - 2*a*b

Here a = x ; b = 4

y = (x - 1)(x² + 4² - 2*x*4)

y = (x - 1)(x² +16  - 2*x*4)

y = (x- 1)(x² +16  - 8x)

y = (x*x² +x*16  - x*8x) - (1*x² +1*16  - 1*8x)

y = (x³ +16x  - 8x²) - (1*x² +1*16  - 1*8x)

y = (x³ +16x  - 8x²) - ( x² + 16  - 8x)

y = (x³ +16x  - 8x²) - ( x² ) - (+16)  - (-8x)

Product of two same signs is positive

y = (x³ +16x  - 8x²) - ( x² ) - (+16) + 8x

Product of two different signs is negative

y = x³ +16x  - 8x² -  x²  - 16 + 8x

y = x³ -  9x²   - 24x - 16

The simplest function is  y = x³ -  9x²   - 24x - 16.

 

Comments

y = x³ +16x  - 8x² -  x²  - 16 + 8x

y = x³ -  9x² + 24x - 16

The simplest function is  y = x³ -  9x² + 24x - 16.

Answer 2

Given function is y = (x - 1)(x - 4)²

Apply (a - b)² = a² + b² - 2*a*b

Here a = x ; b = 4

y = (x - 1)(x² + 4² - 2*x*4)

y = (x - 1)(x² +16  - 2*x*4)

y = (x- 1)(x² +16  - 8x)

y = (x*x² +x*16  - x*8x) - (1*x² +1*16  - 1*8x)

y = (x³ +16x  - 8x²) - ( x² + 16  - 8x)

Product of two same signs is positive

y = (x³ +16x  - 8x²) - ( x² ) - (+16) + 8x

Product of two different signs is negative

y = x³ +16x  - 8x² -  x²  - 16 + 8x

y = x³ -  9x²   + 24x - 16

The simplest function is  y = x³ -  9x²  +  24x - 16.