What is lcm 2x^2-2,4x-4 ?

The solution to lcm 2x^2-2,4x-4 is 4(x+1)(x-1)

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lcm 2x^2-2,4x-4

lcm

2 x^{2} - 2, 4 x - 4

4 (x + 1) (x - 1)

Solution steps

Find Least Common Multiplier of

2 x^{2} - 2, 4 x - 4

Factor

2 x^{2} - 2 : 2 (x + 1) (x - 1)

2 x^{2} - 2

Factor out common term

2

= 2 (x^{2} - 1)

Factor

x^{2} - 1 : (x + 1) (x - 1)

x^{2} - 1

Rewrite

1

1^{2}

= x^{2} - 1^{2}

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

x^{2} - 1^{2} = (x + 1) (x - 1)

= (x + 1) (x - 1)

= 2 (x + 1) (x - 1)

Factor

4 x - 4 : 2^{2} (x - 1)

4 x - 4

Factor out common term

4

= 4 (x - 1)

Factor

4 = 2^{2}

= 2^{2} \cdot (x - 1)

Multiply each factor with the highest power:

2^{2} \cdot (x + 1) \cdot (x - 1)

Simplify

4 (x + 1) (x - 1)

\frac{40}{8}

5 - 2 \cdot 3 + 6 (3^{2} + 1)

(3 - 1)^{2}

3 \cdot 5^{2}

12 + 12