What is lcm x^2+2x+1,x^2-6x+9 ?

The solution to lcm x^2+2x+1,x^2-6x+9 is (x+1)^2(x-3)^2

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lcm x^2+2x+1,x^2-6x+9

lcm

x^{2} + 2 x + 1, x^{2} - 6 x + 9

(x + 1)^{2} (x - 3)^{2}

Solution steps

Find Least Common Multiplier of

x^{2} + 2 x + 1, x^{2} - 6 x + 9

Factor

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

x^{2} + 2 x + 1

Rewrite

x^{2} + 2 x + 1

x^{2} + 2 x \cdot 1 + 1^{2}

x^{2} + 2 x + 1

Rewrite

1

1^{2}

= x^{2} + 2 x + 1^{2}

Rewrite

2 x

2 x \cdot 1

= x^{2} + 2 x \cdot 1 + 1^{2}

= x^{2} + 2 x \cdot 1 + 1^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = x, b = 1

= (x + 1)^{2}

Factor

x^{2} - 6 x + 9 : (x - 3)^{2}

x^{2} - 6 x + 9

Rewrite

x^{2} - 6 x + 9

x^{2} - 2 x \cdot 3 + 3^{2}

x^{2} - 6 x + 9

Rewrite

9

3^{2}

= x^{2} - 6 x + 3^{2}

Rewrite

6 x

2 x \cdot 3

= x^{2} - 2 x \cdot 3 + 3^{2}

= x^{2} - 2 x \cdot 3 + 3^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = x, b = 3

= (x - 3)^{2}

Multiply each factor with the highest power:

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

0.875

\frac{8}{2} \cdot (2 + 2)

- 2 (4)^{2}

\frac{6}{2} (2 + 1)

\frac{180}{5}

What is lcm x^2+2x+1,x^2-6x+9 ?
The solution to lcm x^2+2x+1,x^2-6x+9 is (x+1)^2(x-3)^2