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

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

Evaluate

$49a^{4}-4b^{6}$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

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

Expand $\left(7a^{2}\right)^{2}$.

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

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

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

Calculate $7$ to the power of $2$ and get $49$.

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

Expand $\left(2b^{3}\right)^{2}$.

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

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

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

Calculate $2$ to the power of $2$ and get $4$.

$$49a^{4}-4b^{6}$$

Expand

$49a^{4}-4b^{6}$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

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

Expand $\left(7a^{2}\right)^{2}$.

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

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

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

Calculate $7$ to the power of $2$ and get $49$.

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

Expand $\left(2b^{3}\right)^{2}$.

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

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

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

Calculate $2$ to the power of $2$ and get $4$.

$$49a^{4}-4b^{6}$$