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Vhich of the following is equivalent to -8x^(2)-8xy+12y^(2) ?

Which of the following is equivalent to −8x2−8xy+12y2 -8 x^{2}-8 x y+12 y^{2} ?

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Full solution

Q. Which of the following is equivalent to −8x2−8xy+12y2 -8 x^{2}-8 x y+12 y^{2} ?
  1. Factor out GCF: Factor out the greatest common factor from each term.\newline−8x2−8xy+12y2-8x^2 - 8xy + 12y^2\newline= −4(2x2+2xy−3y2)-4(2x^2 + 2xy - 3y^2)
  2. Pattern in Quadratic: Look for a pattern in the quadratic expression inside the parentheses. \newline2x2+2xy−3y22x^2 + 2xy - 3y^2\newlineThis looks like it might be factorable using the middle term breaking method.
  3. Factor Quadratic: Factor the quadratic expression.\newline2x2+2xy−3y22x^2 + 2xy - 3y^2\newline= 2x2+3xy−xy−3y22x^2 + 3xy - xy - 3y^2\newline= (2x2+3xy)−(xy+3y2)(2x^2 + 3xy) - (xy + 3y^2)\newline= x(2x+3y)−y(x+3y)x(2x + 3y) - y(x + 3y)\newline= (x−y)(2x+3y)(x - y)(2x + 3y)

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