Factorize using identities (i) 1-64x³+48x²-12x

(1 - 4x)³

Step-by-step explanation:

The first 2 terms are a difference of cubes and factor in general as

a³ - b³ = (a - b)(a² + ab + b²), thus

1 - 64x³

= 1³ - (4x)³

= (1 - 4x)(1 + 4x + 16x²)

Thus

1 - 64x³ + 48x² - 12x ← factor out 12x from each of the 2 terms

= (1 - 4x)(1 + 4x + 16x²) + 12x(4x - 1) ← factor out - 1 from (4x - 1)

= (1 - 4x)(1 + 4x + 16x²) - 12x(1 - 4x) ← factor out (1 - 4x) from the terms

= (1 - 4x)(1 + 4x + 16x² - 12x)

= (1 - 4x)(1 - 8x + 16x²) ← perfect square

= (1 - 4x)(1 - 4x)²

= (1 - 4x)³  ← in factored form

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

answer: i'm not going to give you the answer, but some hints to work it out.

step-by-step explanation: so, if there is a straight line that means that the line angle is 180°. so we subtract the 2 angle measures provided, (15 and 38) from 180. so the answer is 180 - (38 + 15). (you have to solve the equation)