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Question
hello scott, I am having some trouble with simplifying these equations, i have given them ago by myself and i cant seem to get the right answer. please help. :)
thank you.
1. 5mn - n(6m - 2m² )
2. 4ab² + 5ab² - (6a²)³
3. 4x² + 3x(-9x + 6)
4. 5m²n³ - (6mn - 4m² n³ + 3 ) + 6
5. -3x6 + (4x³)2
It should be noted that
1) when 4 is cubed, it can be written as 4^3, so 4^3 = 4*4*4 = 16*6 = 64.
2) when we have (a^3)^2, that is (a*a*a)(a*a*a) = a^6.
In other words, the exponets in the original problem are multiplied together.
3) The final note is that when the factors are the same in each term,
the terms can be added together.
1. For 5mn - n(6m - 2m²), multiply it out to 5mn - 6mn - 2nm².
Subtract the first two terms and keep the 3rd, giving -mn - 2mn².
Once this has been done, factor out a -mn giving -mn(1 + 2n).
2. For 4ab² + 5ab² - (6a²)³, the 1st two terms can be added to together,
giving 9ab² - (6a²)³. When 6 is cubed, that is 6*6*6 = 216.
When a² is cubed, you get a²*a²*a² = a^6.
That makes it into 9ab² - 216a^6.
The 9a is in both terms, and results in 9a(b - 24a^5).
3. 4x² + 3x(-9x + 6)
Multiply out the parenthesis, giving 4x² - 37x² + 18x.
Combine the first two term and get - 33x² + 18x.
4. 5m²n³ - (6mn - 4m²n³ + 3 ) + 6
Carry the minus sign out fron to every term in the parenthesis.
This gives 5m²n³ - 6mn + 4m²n³ - 3 + 6.
The 1st and 3rd terms can be combined and the last two terms can be combined.
Since 5m²n³ + 4m²n³ = 9m²n³ and -3+6 = 3, we have 9m²n³ - 6mn + 3.
The 3 can be factored out, giving 3(3m²n³ - 2mn + 1).
5. I will assume the last one is -3x^6 + (4x³)^2.
This makes the problem -3x^6 + 4x^6 = x^6.
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Scott A Wilson
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