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What is the factored form of 15y2−8yz−12z215y^2 - 8yz - 12z^2?

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Full solution

Q. What is the factored form of 15y2−8yz−12z215y^2 - 8yz - 12z^2?
  1. Identify coefficients: Identify the coefficients for factoring: a=15a = 15, b=−8b = -8, c=−12c = -12.
  2. Find two numbers: Find two numbers that multiply to acac (15×−12=−18015 \times -12 = -180) and add to bb (−8-8). The numbers are 1010 and −18-18.
  3. Rewrite middle term: Rewrite the middle term using the numbers found: 15y2+10yz−18yz−12z215y^2 + 10yz - 18yz - 12z^2.
  4. Factor by grouping: Factor by grouping: (15y2+10yz)+(−18yz−12z2)(15y^2 + 10yz) + (-18yz - 12z^2).
  5. Factor out common terms: Factor out the common terms from each group: 5y(3y+2z)−6z(3y+2z)5y(3y + 2z) - 6z(3y + 2z).
  6. Factor out common binomial: Factor out the common binomial: (5y−6z)(3y+2z)(5y - 6z)(3y + 2z).

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