Solve (a ^ 2 - 7b ^ 3) ^ 2 + (a ^ 2 + 7b ^ 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

$$(a^{2}-7b^{3})^{2}+(a^{2}+7b^{3})^{2}$$

Evaluate

$2\left(a^{4}+49b^{6}\right)$

Solution Steps

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(a^{2}-7b^{3}\right)^{2}$.

$$\left(a^{2}\right)^{2}-14a^{2}b^{3}+49\left(b^{3}\right)^{2}+\left(a^{2}+7b^{3}\right)^{2}$$

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

$$a^{4}-14a^{2}b^{3}+49\left(b^{3}\right)^{2}+\left(a^{2}+7b^{3}\right)^{2}$$

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

$$a^{4}-14a^{2}b^{3}+49b^{6}+\left(a^{2}+7b^{3}\right)^{2}$$

Use binomial theorem $\left(p+q\right)^{2}=p^{2}+2pq+q^{2}$ to expand $\left(a^{2}+7b^{3}\right)^{2}$.

$$a^{4}-14a^{2}b^{3}+49b^{6}+\left(a^{2}\right)^{2}+14a^{2}b^{3}+49\left(b^{3}\right)^{2}$$

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

$$a^{4}-14a^{2}b^{3}+49b^{6}+a^{4}+14a^{2}b^{3}+49\left(b^{3}\right)^{2}$$

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

$$a^{4}-14a^{2}b^{3}+49b^{6}+a^{4}+14a^{2}b^{3}+49b^{6}$$

Combine $a^{4}$ and $a^{4}$ to get $2a^{4}$.

$$2a^{4}-14a^{2}b^{3}+49b^{6}+14a^{2}b^{3}+49b^{6}$$

Combine $-14a^{2}b^{3}$ and $14a^{2}b^{3}$ to get $0$.

$$2a^{4}+49b^{6}+49b^{6}$$

Combine $49b^{6}$ and $49b^{6}$ to get $98b^{6}$.

$$2a^{4}+98b^{6}$$

Expand

$2a^{4}+98b^{6}$

Solution Steps

Use binomial theorem $\left(p-q\right)^{2}=p^{2}-2pq+q^{2}$ to expand $\left(a^{2}-7b^{3}\right)^{2}$.

$$\left(a^{2}\right)^{2}-14a^{2}b^{3}+49\left(b^{3}\right)^{2}+\left(a^{2}+7b^{3}\right)^{2}$$

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

$$a^{4}-14a^{2}b^{3}+49\left(b^{3}\right)^{2}+\left(a^{2}+7b^{3}\right)^{2}$$

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

$$a^{4}-14a^{2}b^{3}+49b^{6}+\left(a^{2}+7b^{3}\right)^{2}$$

Use binomial theorem $\left(p+q\right)^{2}=p^{2}+2pq+q^{2}$ to expand $\left(a^{2}+7b^{3}\right)^{2}$.

$$a^{4}-14a^{2}b^{3}+49b^{6}+\left(a^{2}\right)^{2}+14a^{2}b^{3}+49\left(b^{3}\right)^{2}$$

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

$$a^{4}-14a^{2}b^{3}+49b^{6}+a^{4}+14a^{2}b^{3}+49\left(b^{3}\right)^{2}$$

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

$$a^{4}-14a^{2}b^{3}+49b^{6}+a^{4}+14a^{2}b^{3}+49b^{6}$$

Combine $a^{4}$ and $a^{4}$ to get $2a^{4}$.

$$2a^{4}-14a^{2}b^{3}+49b^{6}+14a^{2}b^{3}+49b^{6}$$

Combine $-14a^{2}b^{3}$ and $14a^{2}b^{3}$ to get $0$.

$$2a^{4}+49b^{6}+49b^{6}$$

Combine $49b^{6}$ and $49b^{6}$ to get $98b^{6}$.

$$2a^{4}+98b^{6}$$