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(1). \( 3 v^{4}-6 v w \) 2) \( 4 a^{3} b-8 a b^{3} \)

Ask by Boone Beck. in Switzerland
Jan 21,2025

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1. \( 3v^{4} - 6v w = 3v (v^{3} - 2w) \) 2. \( 4a^{3}b - 8a b^{3} = 4ab (a^{2} - 2b^{2}) \)

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Mind Expander

Let's dive into the magic of factoring! For the expression \( 3v^{4}-6vw \), you can factor out a common term. Notice that both terms share a factor of \( 3v \). This gives you \( 3v(v^3 - 2w) \). Voila! You've simplified it. Now, looking at \( 4a^{3}b-8ab^{3} \), you can reveal its inner beauty by factoring out the greatest common factor, which is \( 4ab \). This simplifies it to \( 4ab(a^2 - 2b^2) \). Factoring is like peeling the layers of an onion—each layer reveals a little more about the equation!

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