equations, GFC and LCM

Question

 

1.  Did I solve the GCF and LCF for 28, 35 and 42?

 

        28 = 2^2 x 7        35 = 5 x 7             42 = 2^2 x 2^2 x 2 x 3

 

    GCF = 2^2 x 3

    LCF = 2x^2 x 5 x 7 x 2 x 3 =  2,100

 

2.  I need help finding the LCF and GCF for 9x^2y and 36xy^3

 

3.  I need help multiplying this problem, (ab-2)(ab+2).

 

    I started with ab(ab + 1) -2(ab+2)

 

thanks

Answer 1

1) To compute the GCF(28,35,42), break each number into its prime factors:

 

28 = 2²*7, 35 = 5*7, 42=2*3*7 (not 2⁵*3 like you have)

 

The GCF(28,35,42) = 7

 

    The LCM is computed by multiplying the highest power of each unique prime number together:

 

LCM(28,35,42) = 2²*7*5*3 = 420

 

2) GCF(9x²2y, 36xy³) = GCF(18x²y, 36xy³)

 

18x2y = 3²*2*x²*y,  36xy³ = 3²*2²*x*y³

 

GCF = 3²*2*x*y = 18xy

 

LCM = 3²*2²*x²*y³ = 36x²y³

 

3)  To multiply (ab + 1)(ab - 1), use the FOIL (first, outer, inner, last) method:

 

(ab + 1)(ab - 1) = (ab)(ab) + (ab)(-1) + (ab)(1) + (1)(-1) = a²b² - 1