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

The solution to expand (3a^2-a+5)^2 is 9a^4-6a^3+31a^2-10a+25

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

expand

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

9 a^{4} - 6 a^{3} + 31 a^{2} - 10 a + 25

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

= 3 a^{2} \cdot 3 a^{2} + 3 a^{2} (- a) + 3 a^{2} \cdot 5 - a \cdot 3 a^{2} - a (- a) - a \cdot 5 + 5 \cdot 3 a^{2} + 5 (- a) + 5 \cdot 5

Simplify

3 a^{2} \cdot 3 a^{2} + 3 a^{2} (- a) + 3 a^{2} \cdot 5 - a \cdot 3 a^{2} - a (- a) - a \cdot 5 + 5 \cdot 3 a^{2} + 5 (- a) + 5 \cdot 5 : 9 a^{4} - 6 a^{3} + 31 a^{2} - 10 a + 25

= 9 a^{4} - 6 a^{3} + 31 a^{2} - 10 a + 25

\frac{2}{3} \div \frac{3}{2}

2 a + 2 a

7 a^{2} (b)

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

\frac{7}{12} + \frac{7}{20}

What is expand (3a^2-a+5)^2 ?
The solution to expand (3a^2-a+5)^2 is 9a^4-6a^3+31a^2-10a+25