math help 10 ptz will be awarded?

Question

1. pr^2-arm+prm-ar^2

2. 2x^3z-4x^2z+30xz-60z

please explain how to do these not just the answer thanks

Answer 1

Guess yu want to factor the expressions

1. pr^2 - arm + prm - ar^2

Rearrange and factor by grouping

pr^2 - ar^2 + prm - arm
r^2(p - a) + rm(p - a)
(r^2 + r)(p - a)

r(r + 1)(p - a)

2. 2x^3z - 4x^2z + 30xz - 60z

2z(x^3 - 2x^2 + 15x - 30)
2z[x^2(x - 2) + 15(x - 2)]

2z(x^2 + 15)(x - 2)

Answer 2

1) first rearrange, put the squared terms together like this:

pr² - ar² - arm + prm
then factor out common terms:

r²(p-a) - mr(p-a)

again factor out the common term (p-a)

(p-a)(r² - rm)

now the r is common in the second term
(p-a)r(r-m) = r(p-a)(r-m)


2) since z and 2 are common to all, take them out first:

2z (x³ - 2x² + 15x - 30)

from hre we can go 2 ways either:
we break up the second term into 2 groups like this

2z [(x³ - 2x²) + (15x - 30)]
then factor out common terms to get:
2z (x²[x - 2] + 15[x - 2])
agaun the x-2 is common and can be brought out to get
2z (x² + 15)(x - 2)


OR x is common to the first 3 in the parenthesis:

2z [ x(x² - 2x+ 15) - 30 ]