What is expand (5a+a^2+a^3)^2 ?

The solution to expand (5a+a^2+a^3)^2 is a^6+2a^5+11a^4+10a^3+25a^2

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expand (5a+a^2+a^3)^2

expand

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

a^{6} + 2 a^{5} + 11 a^{4} + 10 a^{3} + 25 a^{2}

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(5 a + a^{2} + a^{3})^{2} = (5 a + a^{2} + a^{3}) (5 a + a^{2} + a^{3})

= (5 a + a^{2} + a^{3}) (5 a + a^{2} + a^{3})

Distribute parentheses

= 5 a \cdot 5 a + 5 a a^{2} + 5 a a^{3} + a^{2} \cdot 5 a + a^{2} a^{2} + a^{2} a^{3} + a^{3} \cdot 5 a + a^{3} a^{2} + a^{3} a^{3}

Simplify

5 a \cdot 5 a + 5 a a^{2} + 5 a a^{3} + a^{2} \cdot 5 a + a^{2} a^{2} + a^{2} a^{3} + a^{3} \cdot 5 a + a^{3} a^{2} + a^{3} a^{3} : a^{6} + 2 a^{5} + 11 a^{4} + 10 a^{3} + 25 a^{2}

= a^{6} + 2 a^{5} + 11 a^{4} + 10 a^{3} + 25 a^{2}

\frac{x ^{8} - y ^{8}}{x + y}

\frac{12}{4} + 2 \frac{1}{2} - 3

x^{4} \cdot x^{- 4}

(1 - u^{2})^{4}

9^{\frac{1}{1}}

What is expand (5a+a^2+a^3)^2 ?
The solution to expand (5a+a^2+a^3)^2 is a^6+2a^5+11a^4+10a^3+25a^2