If A=3x+4 and B=x^2+2 and C=x^2+3x-2, find the following:
1. AC+B
2. (A+B)(B-C)
3. ABC
just substitute in. For example,
ABC = (3x+4)(x^2+2)(x^2+3x-2)
= 3x^5+13x^4+12x^3+18x^2+12x-16
what do you get for the others?
1. 17x^2+6x-6
2. 3x^3+9x^2+18x
did you get the same?
I get
AC+B = 3x^^3+14x^2+6x-6
AC has to be 3rd degree, since A is 1 and C is 2
(A+B)(B-C)
= -3x^3-5x^2-6x+24
Somewhere you're messing up. Visit calc101.com and click on the "long multiplication" link, and it will show all the details of polynomial multiplication.
To find the values of the given expressions, we need to substitute the given expressions for A, B, and C into the respective formulas or equations. Let's substitute the values and simplify each expression step by step:
1. AC + B:
Substitute A = 3x + 4 and C = x^2 + 3x - 2 into the expression AC + B:
AC + B = (3x + 4)(x^2 + 3x - 2) + (x^2 + 2)
Now, distribute the multiplication:
AC + B = (3x + 4)(x^2) + (3x + 4)(3x) + (3x + 4)(-2) + x^2 + 2
Simplify each term:
AC + B = 3x^3 + 4x^2 + 9x^2 + 12x + 6x + 8 - 6x - 8 + x^2 + 2
Combine like terms:
AC + B = 3x^3 + 14x^2 + 12x
2. (A + B)(B - C):
Substitute A = 3x + 4, B = x^2 + 2, and C = x^2 + 3x - 2 into the expression (A + B)(B - C):
(A + B)(B - C) = (3x + 4 + x^2 + 2)((x^2 + 2) - (x^2 + 3x - 2))
Simplify the expression inside the parentheses:
(A + B)(B - C) = (x^2 + 3x + 6)((x^2 + 2) - (x^2 + 3x - 2))
Now, distribute the multiplication:
(A + B)(B - C) = (x^2 + 3x + 6)(x^2 - x^2 - 3x + 2 + 2)
Simplify each term:
(A + B)(B - C) = (x^2 + 3x + 6)(0 - 3x + 4)
Distribute the multiplication:
(A + B)(B - C) = 0(x^2) - 3x(x^2) + 4(x^2) + 0(x) - 3x(3x) + 4(3x) + 0(6) - 3x(0) + 4(0)
Simplify each term:
(A + B)(B - C) = 0 - 3x^3 + 4x^2 + 0 - 3x^2 + 12x + 0 - 0 + 0
Combine like terms:
(A + B)(B - C) = -3x^3 + x^2 + 12x
3. ABC:
Substitute A = 3x + 4, B = x^2 + 2, and C = x^2 + 3x - 2 into the expression ABC:
ABC = (3x + 4)(x^2 + 2)(x^2 + 3x - 2)
Now, distribute the multiplication:
ABC = (3x + 4)(x^2)(x^2 + 3x - 2) + (3x + 4)(2)(x^2 + 3x - 2)
Simplify each term:
ABC = (3x^3 + 4x^2)(x^2 + 3x - 2) + 2(3x + 4)(x^2 + 3x - 2)
Distribute the multiplication:
ABC = 3x^5 + 9x^4 - 6x^3 + 4x^4 + 12x^3 - 8x^2 + 6x^3 + 18x^2 - 12x + 8x^2 + 24x - 16
Combine like terms:
ABC = 3x^5 + 13x^4 + 12x^3 + 16x^2 + 12x - 16
Therefore:
1. AC + B = 3x^3 + 14x^2 + 12x
2. (A + B)(B - C) = -3x^3 + x^2 + 12x
3. ABC = 3x^5 + 13x^4 + 12x^3 + 16x^2 + 12x - 16