This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Rearrange the terms to group the perfect square trinomial. The given expression is 4p^2 - 12pq - m^2 + 9q^2. We can rearrange the terms to group the p and q terms together: 4p^2 - 12pq + 9q^2 - m^2 Step 2: Factor the perfect square trinomial. The first three terms, 4p^2 - 12pq + 9q^2, form a perfect square trinomial. Recognize that 4p^2 = (2p)^2 and 9q^2 = (3q)^2. The middle term is -12pq, which is 2 × (2p) × (-3q). So, the trinomial can be factored as (2p - 3q)^2. The expression becomes: (2p - 3q)^2 - m^2 Step 3: Apply the difference of squares formula. The expression is now in the form A^2 - B^2, where A = (2p - 3q) and B = m. The difference of squares formula is A^2 - B^2 = (A - B)(A + B). Substitute A and B into the formula: ((2p - 3q) - m)((2p - 3q) + m) Step 4: Simplify the factored expression. (2p - 3q - m)(2p - 3q + m) The factored expression is: (2p - 3q - m)(2p - 3q + m) That's 2 down. 3 left today — send the next one.