What is (x^2-4x+4)(x^2-4x+4)+13(x^2-4x+4)+36 ?

The solution to (x^2-4x+4)(x^2-4x+4)+13(x^2-4x+4)+36 is x^4-8x^3+37x^2-84x+104

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simplify (x^2-4x+4)(x^2-4x+4)+13(x^2-4x+4)+36

simplify

(x^{2} - 4 x + 4) (x^{2} - 4 x + 4) + 13 (x^{2} - 4 x + 4) + 36

x^{4} - 8 x^{3} + 37 x^{2} - 84 x + 104

Solution steps

(x^{2} - 4 x + 4) (x^{2} - 4 x + 4) + 13 (x^{2} - 4 x + 4) + 36

Apply exponent rule:

aa = a^{2}

(x^{2} - 4 x + 4) (x^{2} - 4 x + 4) = (x^{2} - 4 x + 4)^{2}

= (x^{2} - 4 x + 4)^{2} + 13 (x^{2} - 4 x + 4) + 36

Expand

(x^{2} - 4 x + 4)^{2} : x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16

= x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16 + 13 (x^{2} - 4 x + 4) + 36

Expand

13 (x^{2} - 4 x + 4) : 13 x^{2} - 52 x + 52

= x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16 + 13 x^{2} - 52 x + 52 + 36

Group like terms

= x^{4} - 8 x^{3} + 24 x^{2} + 13 x^{2} - 32 x - 52 x + 16 + 52 + 36

Add similar elements:

24 x^{2} + 13 x^{2} = 37 x^{2}

= x^{4} - 8 x^{3} + 37 x^{2} - 32 x - 52 x + 16 + 52 + 36

Add similar elements:

- 32 x - 52 x = - 84 x

= x^{4} - 8 x^{3} + 37 x^{2} - 84 x + 16 + 52 + 36

Add the numbers:

16 + 52 + 36 = 104

= x^{4} - 8 x^{3} + 37 x^{2} - 84 x + 104

(3 x^{2} + 5 x + 9) (6 x - 8)

((4 x)^{2} - (3 b)^{4})^{2}

\frac{1}{6} \cdot 8

\frac{x + 5}{x ^{2} + 6 x + 5}

\frac{2}{3} \cdot \frac{1}{4} \cdot \frac{3}{5}

What is (x^2-4x+4)(x^2-4x+4)+13(x^2-4x+4)+36 ?
The solution to (x^2-4x+4)(x^2-4x+4)+13(x^2-4x+4)+36 is x^4-8x^3+37x^2-84x+104