Hello. I have these 2 questions and I was wondering on how to solve them.
I am able to get the answer for the first one, but is there perhaps a shorter method to achieve the answer?
Simplify the following:
(x+2)²(x-1)² - (x-4)²(x+4)²
Answer: 2x³ + 29x² - 4x - 252
I was able to solve but it was a lot of steps and there was too much room for error. Is there perhaps a trick to solving these types of questions?
And I need to factor this.
(m-n)² - (2m+3n)²
Answer: -(m+4n)(3m+2n)
I was not able to get this answer and so if someone can show me their steps with a brief explanation, I would really appreciate it.
I am able to get the answer for the first one, but is there perhaps a shorter method to achieve the answer?
Simplify the following:
(x+2)²(x-1)² - (x-4)²(x+4)²
Answer: 2x³ + 29x² - 4x - 252
I was able to solve but it was a lot of steps and there was too much room for error. Is there perhaps a trick to solving these types of questions?
And I need to factor this.
(m-n)² - (2m+3n)²
Answer: -(m+4n)(3m+2n)
I was not able to get this answer and so if someone can show me their steps with a brief explanation, I would really appreciate it.
-
(x+2)²(x-1)² - (x-4)²(x+4)²
I can write it as
[(x + 2)(x - 1)]² - [(x - 4)(x + 4)]²
Now it is difference of the squares but before I use differences of the square dentity, I will work with the terms inside the brackets first.
(x² + x - 2)² - (x² - 16)²
[x² + x - 2 - (x² - 16)][x² + x - 2 + x² - 16]
(x + 14)(2x² + x - 18)
Expand this
x(2x² + x - 18) + 14(2x² + x - 18)
2x³ + x² - 18x + 28x² + 14x - 252
2x³ + 29x² - 4x - 252
to me I think this is much shorter process.
-----------
The second one is also differences of the squares
[(m - n) - (2m + 3n)][(m - n) + (2m + 3n)]
(m - n - 2m - 3n)(m - n + 2m + 3n)
(-m - 4n)(3m + 2n)
Now factor -1 from (-m - 4n)
-(m + 4n)(3m + 2n)
I can write it as
[(x + 2)(x - 1)]² - [(x - 4)(x + 4)]²
Now it is difference of the squares but before I use differences of the square dentity, I will work with the terms inside the brackets first.
(x² + x - 2)² - (x² - 16)²
[x² + x - 2 - (x² - 16)][x² + x - 2 + x² - 16]
(x + 14)(2x² + x - 18)
Expand this
x(2x² + x - 18) + 14(2x² + x - 18)
2x³ + x² - 18x + 28x² + 14x - 252
2x³ + 29x² - 4x - 252
to me I think this is much shorter process.
-----------
The second one is also differences of the squares
[(m - n) - (2m + 3n)][(m - n) + (2m + 3n)]
(m - n - 2m - 3n)(m - n + 2m + 3n)
(-m - 4n)(3m + 2n)
Now factor -1 from (-m - 4n)
-(m + 4n)(3m + 2n)
-
you must achieve it step by step