Factor p^3 + 125?

Question

Factor p^3 + 125q^3

Answer 1

p³ + 125
= p³ + p³
= (p + 5)(p - 5p + 25)

This is because (x³ + a³) = (x + a)(x² - ax + a²)
and (x³ - a³) = (x - a)(x² + ax + a²)

Answer 2

Use the perfect cube formula for binomials
a^3 + b^3 = (a + b)(a^2 - ab + b^2)

p^3 + 125
P^3 + 5^3 so the a is p and the b is 5 in the formula
(p + 5) (p^2 - 5p + 25)

Answer 3

This is what is known as factor a sum of cubes. The trick to factor sums and differences of cubes is the following:

1) Take the cube root of each term; place in first set of brackets.

2) Square the first.
3) Negative product.
4) Square the last.

So for p^3 + 125:

"Take the cube root of each term"

The cube root of p^3 is p, and the cube root of 125 is 5, so we have:

(p + 5) (? + ? + ?)

"Square the first"

Square the first term in the first set of brackets.

(p + 5)(p^2 + ? + ?)

"Negative product"

Take the product of both of the terms, and then negate it. p times 5 is 5p, negated is -5p.

(p + 5)(p^2 - 5p + ?)

"Square the last"

Square the 2nd term. 5 squared is 25.

(p + 5)(p^2 - 5p + 25)

Answer 4

Rule:
a^3 + b^3 = (a + b)(a^2 - ab + b^2)

So: p^3 + 125
(p + 5) (p^2 - 5p + 25)

Answer 5

well first of all you have to get 125 to be a cube root which is 5
so you would have
p^3 + 5^3
then you take out the cubes and that's your short parentheses.
so (p+5)
then you take the square of the first term, change the sign, multiply the two terms in the first parentheses, and square the last term...like so
(p+5) (p^2 - 5p + 25)
remember SOAP
S - square (first term)
O - opposite (sign)
AP - always positive (any number squared has to be positive)

Answer 6

p^3 + 125 = (p + 5) ( p - 2.5 + Q) (p - 2.5 -Q)

Q = 5 sin (60 deg) = 4.330127...

Answer 7

p^3+5^3
=(p+5)(p^2-5p+25)

remember a^3-b^3=?

Answer 8

2+2is4!

Answer 9

p= 41.666