Answer
$$(16d^2+25)(4d+5)(4d-5)=256d^4-625$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(16d^2+25)(4d+5)(4d-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(64d^3+80d^2+100d+125)(4d-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}256d^4-625\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{16d^2+25}\right) $ by each term in $ \left( 4d+5\right) $. $$ \left( \color{blue}{16d^2+25}\right) \cdot \left( 4d+5\right) = 64d^3+80d^2+100d+125 $$ |
| ② | Multiply each term of $ \left( \color{blue}{64d^3+80d^2+100d+125}\right) $ by each term in $ \left( 4d-5\right) $. $$ \left( \color{blue}{64d^3+80d^2+100d+125}\right) \cdot \left( 4d-5\right) = \\ = 256d^4 -\cancel{320d^3}+ \cancel{320d^3} -\cancel{400d^2}+ \cancel{400d^2} -\cancel{500d}+ \cancel{500d}-625 $$ |
| ③ | Combine like terms: $$ 256d^4 \, \color{blue}{ -\cancel{320d^3}} \,+ \, \color{blue}{ \cancel{320d^3}} \, \, \color{green}{ -\cancel{400d^2}} \,+ \, \color{green}{ \cancel{400d^2}} \, \, \color{blue}{ -\cancel{500d}} \,+ \, \color{blue}{ \cancel{500d}} \,-625 = 256d^4-625 $$ |
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