Question

Express the following in the form ax2+bx+c=0:

(x+3)(3x - 2)=(4x +5)(2x-3)
(3x+2)^2=(x+2)(x-3)
(x+1)(x+2)=(2x-1)(x-2)

Answer 1

To express the given equations in the form ax^2+bx+c=0, expand the products on both sides and then rearrange the terms. The equations become 8x^2 - 26x + 21 = 0, 8x^2 + 13x + 10 = 0, and x^2 + 2x = 0.

Step-by-step explanation:

To express the given equations in the form ax^2+bx+c=0, we can expand the products on both sides of the equation and then rearrange the terms. Let's take each equation one by one:

1. (x+3)(3x - 2)=(4x +5)(2x-3)
   Expanding both sides:
   3x^2 - 2x + 9x - 6 = 8x^2 - 12x + 10x - 15
   Simplifying:
   11x - 6 = 8x^2 - 2x - 15
   Moving all terms to one side:
   8x^2 - 15x - 11x + 6 + 15 = 0
   Combining like terms:
   8x^2 - 26x + 21 = 0
2. (3x+2)^2=(x+2)(x-3)
   Expanding the left side:
   9x^2 + 12x + 4 = x^2 - 3x + 2x - 6
   Combining like terms:
   9x^2 + 12x + 4 = x^2 - x - 6
   Moving all terms to one side:
   9x^2 - x^2 + 12x + x + 4 + 6 = 0
   Combining like terms:
   8x^2 + 13x + 10 = 0
3. (x+1)(x+2)=(2x-1)(x-2)
   Expanding both sides:
   x^2 + 2x + x + 2 = 2x^2 - 4x - x + 2
   Simplifying:
   x^2 + 3x + 2 = 2x^2 - 5x + 2
   Moving all terms to one side:
   2x^2 - x^2 + 5x - 3x + 2 - 2 = 0
   Combining like terms:
   x^2 + 2x = 0

Answer 2

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