What is (sqrt(x)+2)(sqrt(x)-2)(x+4)+(x+4)(4-x) ?

The solution to (sqrt(x)+2)(sqrt(x)-2)(x+4)+(x+4)(4-x) is 0

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simplify (sqrt(x)+2)(sqrt(x)-2)(x+4)+(x+4)(4-x)

simplify

(x + 2) (x - 2) (x + 4) + (x + 4) (4 - x)

0

Solution steps

(x + 2) (x - 2) (x + 4) + (x + 4) (4 - x)

Apply Difference of Two Squares

(x + 2) (x - 2) : x - 4

= (x - 4) (x + 4) + (x + 4) (4 - x)

Expand

(x - 4) (x + 4) : x^{2} - 16

= x^{2} - 16 + (x + 4) (4 - x)

Expand

(x + 4) (4 - x) : 16 - x^{2}

= x^{2} - 16 + 16 - x^{2}

Group like terms

= x^{2} - x^{2} - 16 + 16

Add similar elements:

x^{2} - x^{2} = 0

= - 16 + 16

16 - 16 = 0

= 0

\frac{4}{5} \cdot 15

\frac{a}{a + b - 1}

x + \frac{3}{2}

(- 5 - 7 i)^{2}

36 x^{3} y^{9}

What is (sqrt(x)+2)(sqrt(x)-2)(x+4)+(x+4)(4-x) ?
The solution to (sqrt(x)+2)(sqrt(x)-2)(x+4)+(x+4)(4-x) is 0