What is a(a+1)(a+2)(a+3)-15 ?

The solution to a(a+1)(a+2)(a+3)-15 is a^4+6a^3+11a^2+6a-15

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simplify a(a+1)(a+2)(a+3)-15

simplify

a (a + 1) (a + 2) (a + 3) - 15

a^{4} + 6 a^{3} + 11 a^{2} + 6 a - 15

Solution steps

a (a + 1) (a + 2) (a + 3) - 15

Apply FOIL method

(a + 1) (a + 2) : a^{2} + 3 a + 2

= a (a^{2} + 3 a + 2) (a + 3) - 15

Expand

a (a + 3) : a^{2} + 3 a

= (a^{2} + 3 a) (a^{2} + 3 a + 2) - 15

Distribute parentheses

= a^{2} a^{2} + a^{2} \cdot 3 a + a^{2} \cdot 2 + 3 a a^{2} + 3 a \cdot 3 a + 3 a \cdot 2 - 15

Simplify

a^{2} a^{2} + a^{2} \cdot 3 a + a^{2} \cdot 2 + 3 a a^{2} + 3 a \cdot 3 a + 3 a \cdot 2 : a^{4} + 6 a^{3} + 11 a^{2} + 6 a

= a^{4} + 6 a^{3} + 11 a^{2} + 6 a - 15

3 \frac{x ^{2}}{x} + \frac{2}{6} \frac{x ^{4}}{( x ^{2} + 5 x + 6 )}

x^{4} - 17 x^{2} y^{2} - 84 y^{4}

\frac{( 24 z ^{2} - 12 z + 6 )}{( - 6 )}

x^{2} - ∣ x ∣ - \frac{12}{x} - 3

(64 a^{2})^{\frac{1}{6}}

What is a(a+1)(a+2)(a+3)-15 ?
The solution to a(a+1)(a+2)(a+3)-15 is a^4+6a^3+11a^2+6a-15