Solve 3(a ^ 2 + 3); (a ^ 2 - 3); (a ^ 2 + 3) ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$3(a^{2}+3); (a^{2}-3); (a^{2}+3)^{2}$$

Evaluate

$3\left(a^{2}-3\right)\left(a^{2}+3\right)^{3}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$3\left(a^{2}+3\right)^{3}\left(a^{2}-3\right)$$

Use binomial theorem $\left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3}$ to expand $\left(a^{2}+3\right)^{3}$.

$$3\left(\left(a^{2}\right)^{3}+9\left(a^{2}\right)^{2}+27a^{2}+27\right)\left(a^{2}-3\right)$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $3$ to get $6$.

$$3\left(a^{6}+9\left(a^{2}\right)^{2}+27a^{2}+27\right)\left(a^{2}-3\right)$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$3\left(a^{6}+9a^{4}+27a^{2}+27\right)\left(a^{2}-3\right)$$

Use the distributive property to multiply $3$ by $a^{6}+9a^{4}+27a^{2}+27$.

$$\left(3a^{6}+27a^{4}+81a^{2}+81\right)\left(a^{2}-3\right)$$

Use the distributive property to multiply $3a^{6}+27a^{4}+81a^{2}+81$ by $a^{2}-3$ and combine like terms.

$$3a^{8}+18a^{6}-162a^{2}-243$$

Expand

$3a^{8}+18a^{6}-162a^{2}-243$

Solution Steps

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$3\left(a^{2}+3\right)^{3}\left(a^{2}-3\right)$$

Use binomial theorem $\left(p+q\right)^{3}=p^{3}+3p^{2}q+3pq^{2}+q^{3}$ to expand $\left(a^{2}+3\right)^{3}$.

$$3\left(\left(a^{2}\right)^{3}+9\left(a^{2}\right)^{2}+27a^{2}+27\right)\left(a^{2}-3\right)$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $3$ to get $6$.

$$3\left(a^{6}+9\left(a^{2}\right)^{2}+27a^{2}+27\right)\left(a^{2}-3\right)$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$3\left(a^{6}+9a^{4}+27a^{2}+27\right)\left(a^{2}-3\right)$$

Use the distributive property to multiply $3$ by $a^{6}+9a^{4}+27a^{2}+27$.

$$\left(3a^{6}+27a^{4}+81a^{2}+81\right)\left(a^{2}-3\right)$$

Use the distributive property to multiply $3a^{6}+27a^{4}+81a^{2}+81$ by $a^{2}-3$ and combine like terms.

$$3a^{8}+18a^{6}-162a^{2}-243$$