Reduce the following rational expression to the lowest form

4x(x - 1)

Step-by-step explanation:

Factor the numerator and denominator

64 - 64x ← factor out 64x from both terms

= 64x( - 1) ← difference of squares

= 64x(x² - 1)(x² + 1) ← x² - 1 is also a difference of squares

= 64x(x - 1)(x + 1)(x² + 1)

---------------------------------

(8x² + 8)(2x + 2) ← factor out 8 and 2 from each factor

= 8(x² + 1) × 2(x + 1)

= 16(x² + 1)(x + 1)

Then expression can be written as

← cancel (x² + 1) and (x + 1) on numerator/ denominator

= ← cancel common factor 16 on numerator/ denominator

= 4x(x - 1)

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct