Factoring Problems: Can you please show me the complete solutions for factoring the following?

Question

1. n(x-y) + (n-1)(y-x)

2. 4a2c2 - (a2-b2+c2)2

* all 2's are exponents

Answer 1

= nx - ny + ny -y - nx + x
= x - y

= 4a^2c^2 - a^4 + 2a^2b^2 - 2a^2c^2 + 2b^2c^2 - b^4 - c^4
= 2a^2c^2 - a^4 + 2a^2b^2 + 2b^2c^2 - b^4 - c^4

Answer 2

it relatively is like this...you get the climate of 6r^2 + 19r - 7..if fixing for r then you definately might desire to apply the quadratic formulation yet once you're purely after the climate, then you definately might desire to apply the trial and mistake approach... permit's use the trial and mistake approach... first checklist the climate of -7 that once achieved like this: (3r-?)(2r+?) or (3r+?)(2r-?) will produce the given.. the climate of -7 are the two +a million,-7 or -a million,7 (multiplying a million and -7 will produce -7 and so as -a million and seven...) so attempt substituting the two aspects: (3r-7)(2r+a million)= multiply the -7 and 2r and u'll get -14r = multiply 3r and a million and u'll get 3r -14r+3r=-11r...11r isn't the middle term of your given so those aspects are no longer the the terrific option ones... attempt the different aspects (3r-a million)(2r+7) = multiply the internal variables: -a million and 2r = -2r = multiply the outer variables: 3r and +7= 21r 21r+(-2r)= 21r-2r= 19r (it relatively is the middle term of the given) so, factoring 6r squared+19r-7, you will get (3r-a million)(2r=7) have been given it? the 2d is 2b^2+9b-35 back checklist the climate of -35: -7 and 5 7 and -5 replace in: (2b-?)(b+?) or (2b+?)(b-?) substituting -7 and 5: (2b+5)(b-7)= multiply the internal variables: 5xb=5b multiply the outer variables: 2bx-7=-14b upload the products: 5b+(-14b)=5b-14b= -9b -9b isn't the middle term of the given so it relatively is faulty replace the different: (2b-5)(b+7)= multiply the internal: -5xb= -5b multiply the outer: 2bx7= 14b upload the products: -5b + 14b = 9b so, the the terrific option answer is: (2b-5)(b+7) desire this helped...=D

Answer 3

1. n(x-y) + (n-1)(y-x)... to change x-y to y-x, multiply by -1
-n(y-x) + (n-1)(y-x).. since (y-x) is common
(y-x)( -n + n - 1)
(y-x)(-1)
(x-y)

2. 4a^2c^2 - (a^2 -b^2 +c^2)^2
(2ac)^2 - (a^2 -b^2 + c^2)^2.... using principle of difference of two squares
(2ac -a^2 +b^2 -c^2)(2ac +a^2 -b^2 + c^2)

Answer 4

1. n(x-y) + (n-1)(y-x)
=n(x-y) - (n-1)(x-y)
=(x-y)(n-n+1)
=x-y

2. 4a^2 c^2 - (a^2-b^2+c^2)^2
=(2ac)^2-(a^2-b^2+c^2)^2
=(2ac-a^2+b^2+c^2)(2ac+a^2-b^2+c^2)

Answer 5

Hey there! This is how i did it:

1. nx-ny+ny-nx+ny+x= x+ny

2. Dunno, sry