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

+1 vote

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  - 8x2x2  - 16 + 8x

y = x3 9x2   - 24x - 16

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

reshown Dec 27, 2012

y = x3 +16x  - 8x2x2  - 16 + 8x

y = x3 9x2 + 24x - 16

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

+1 vote

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  - 8x2x2  - 16 + 8x

y = x3 9x2   + 24x - 16

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