Anybody good at math please help.?

Question

First problem i need help with: (x-3)(x+7)-(x+1)(x+5)= 0
and
Express as a polynomial: The square of n^2+2n-1
The cube of a-3
Subtract the product of 2x-y and x-2y from x^2 +y^2
If anybody can help with any of them i would greatly appreciate it. Thank you!

Answer 1

well for the first one i would say separate them and combine like terms
x^2+4x-21- (x^2+6x+5)=0
x^2+4x-21- x^2-6x-5 = 0
-2x-26 = 0
-2x = 26
x = -13

(n^2+2n-1)^2 = n^4 + 2n^3 - n^2 + 2n^3 + 4n^2 - 2n - n^2 - 2n + 1 =
n^4 + 4n^3 + 2n^2 - 4n +1

First do (a-3)(a-3) = a^2+6a+9
(a^2+6a+9)(a-3) = a^3 + 6a^2 + 9a - 3a^2 - 18a - 27 = a^3 +3a^2 - 9a - 27

(2x - y) (x-2y) = 2x^2 - 4xy - xy +2y^2 = 2x^2 - 5xy + 2y^2
x^2 + y^2 - (2x^2 - 5xy + 2y^2) = x^2 + y^2 - 2x^2 + 5xy - 2y^2 =
5xy - x^2 - y^2

I hope that i showed enough work that you understood what i did and you know how to do these problems so you won't have to ask again.

Answer 2

Problem 1 FOIL
(x - 3)(x + 7) and -(x + 1)(x + 5)

first x * x = x^2 and -x * x = -x^2
outside x * 7 = 7x and -x * 5 = -5x
inside -3 * x = -3x and 1 * x = x
last -3 * 7 = -21 and 1 * 5 = 5

you should now have the following
x^2 + 7x - 3x -21
-x^2 - 5x + x + 5

combine like terms

x^2 +5x - 21
-x^2 -4x + 5

x - 16 = 0
+ 16 = +16
x = 16

Answer 3

first problem:
(x-3)(x+7)- (x+1)(x+5) = 0
therefore (x2 +4x - 21) - (x2 + 6x +5) = 0
therefore -2x - 26 = 0
therefore -2x = 26
therefore x = -13

second problem:
the square of n^2 +2n- 1=
(n^2 + 2n-1)(n^2 + 2n-1)
= n^4 + 2n^3 - n^2 + 2n^3 + 4n^2 - 2n - n^2 - 2n +1
= n^4 + 4n^3 + 2n^2 - 4n + 1

the cube of a-3 =
(a-3)(a-3)(a-3)
=(a^2 - 6a + 9)(a-3)
=a^3 - 3a^2 - 6a^2 + 18a + 9a - 27
=a^3 - 9a^2 + 27a - 27

Subtract the product of 2x-y and x-2y from x^2 +y^2
(2x - y)(x - 2y) - (x^2 + y^2) =
2x^2 - 4xy - xy + 2y^2 - (x^2 + y^2)=
2x^2 - 5xy + 2y^2 - (x^2 + y^2)=
x^2 + y^2 - 5xy

Answer 4

first prob: (x-3)(x+7)-(x+1)(x+5)=0 becomes (x-3)(x+7)=(x+1)(x+5), then multiply on each side (x*x)+(x*7)+(-3*x)+(-3*7)=(x*x)+(x*5)+(1*x)+(1*5), becomes x2-+7x-3x-21=x2+5x+x+5, becomes x2+4x-21=x2+6x+5, sorting out the equation by bringing similar items to one side, x2-x2+4x-6x=5+21, becomes -6x=26, i.e. x=-13