Question

(4x ^3 + 7y ^3z ^4) ^2

Answer 1

16
`x^(6)` + 56x³y³
`z^(4)` + 49
`y^(6)`
`z^(8)`

Explanation:

Note that we are using the rule of exponents

`a^(m)` ×
`a^(n)` ⇔
`a^((m+n))`

Given

(4x³ + 7y³
`z^(4)` )² = (4x³ + 7y³
`z^(4)` )(4x³ + 7y³
`z^(4)` )

Each term in the second factor is multiplied by each term in the first factor, that is

4x³ (4x³ + 7y³
`z^(4)` ) + 7y³
`z^(4)` ( 4x³ + 7y³
`z^(4)` ) ← distribute both parenthesis

= 16
`x^(6)` + 28x³y³
`z^(4)` + 28x³y³
`z^(4)` + 49
`y^(6)`
`z^(8)` ← collect like terms

= 16
`x^(6)` + 56x³y³
`z^(4)` + 49
`y^(6)`
`z^(8)`