Solve (2a + y)(2a - y)(4a ^ 2 + y ^ 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

$$(2a+y)(2a-y)(4a^{2}+y^{2})$$

Evaluate

$16a^{4}-y^{4}$

Solution Steps

Use the distributive property to multiply $2a+y$ by $2a-y$ and combine like terms.

$$\left(4a^{2}-y^{2}\right)\left(4a^{2}+y^{2}\right)$$

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

$$\left(4a^{2}\right)^{2}-\left(y^{2}\right)^{2}$$

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

$$\left(4a^{2}\right)^{2}-y^{4}$$

Expand $\left(4a^{2}\right)^{2}$.

$$4^{2}\left(a^{2}\right)^{2}-y^{4}$$

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

$$4^{2}a^{4}-y^{4}$$

Calculate $4$ to the power of $2$ and get $16$.

$$16a^{4}-y^{4}$$

Expand

$16a^{4}-y^{4}$

Solution Steps

Use the distributive property to multiply $2a+y$ by $2a-y$ and combine like terms.

$$\left(4a^{2}-y^{2}\right)\left(4a^{2}+y^{2}\right)$$

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

$$\left(4a^{2}\right)^{2}-\left(y^{2}\right)^{2}$$

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

$$\left(4a^{2}\right)^{2}-y^{4}$$

Expand $\left(4a^{2}\right)^{2}$.

$$4^{2}\left(a^{2}\right)^{2}-y^{4}$$

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

$$4^{2}a^{4}-y^{4}$$

Calculate $4$ to the power of $2$ and get $16$.

$$16a^{4}-y^{4}$$