Answer:
16[tex]x^{6}[/tex] + 56x³y³[tex]z^{4}[/tex] + 49[tex]y^{6}[/tex][tex]z^{8}[/tex]
Step-by-step explanation:
Note that we are using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
Given
(4x³ + 7y³[tex]z^{4}[/tex] )² = (4x³ + 7y³[tex]z^{4}[/tex] )(4x³ + 7y³[tex]z^{4}[/tex] )
Each term in the second factor is multiplied by each term in the first factor, that is
4x³ (4x³ + 7y³[tex]z^{4}[/tex] ) + 7y³[tex]z^{4}[/tex] ( 4x³ + 7y³[tex]z^{4}[/tex] ) ← distribute both parenthesis
= 16[tex]x^{6}[/tex] + 28x³y³[tex]z^{4}[/tex] + 28x³y³[tex]z^{4}[/tex] + 49[tex]y^{6}[/tex][tex]z^{8}[/tex] ← collect like terms
= 16[tex]x^{6}[/tex] + 56x³y³[tex]z^{4}[/tex] + 49[tex]y^{6}[/tex][tex]z^{8}[/tex]
