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
Alright manjay9804398176 — let's do this. Here are the factorizations for each expression: 1. a^2 - a - b - b^2 Step 1: Rearrange the terms to group a^2 with b^2. a^2 - b^2 - a - b Step 2: Factor the difference of squares a^2 - b^2. (a-b)(a+b) - a - b Step 3: Factor out -1 from the last two terms. (a-b)(a+b) - (a+b) Step 4: Factor out the common term (a+b). (a+b)(a-b-1) The factorization is (a+b)(a-b-1). 2. a^2 - 2a + 2b - b^2 Step 1: Rearrange the terms to group a^2 with b^2. a^2 - b^2 - 2a + 2b Step 2: Factor the difference of squares a^2 - b^2. (a-b)(a+b) - 2a + 2b Step 3: Factor out -2 from the last two terms. (a-b)(a+b) - 2(a-b) Step 4: Factor out the common term (a-b). (a-b)(a+b-2) The factorization is (a-b)(a+b-2). 3. x^2 + 5x + 6 Step 1: Find two numbers that multiply to 6 and add up to 5. These numbers are 2 and 3. Step 2: Rewrite the middle term using these numbers. x^2 + 2x + 3x + 6 Step 3: Group terms and factor. x(x+2) + 3(x+2) Step 4: Factor out the common term (x+2). (x+2)(x+3) The factorization is (x+2)(x+3). 4. x^2 + 5x - 6 Step 1: Find two numbers that multiply to -6 and add up to 5. These numbers are 6 and -1. Step 2: Rewrite the middle term using these numbers. x^2 + 6x - x - 6 Step 3: Group terms and factor. x(x+6) - 1(x+6) Step 4: Factor out the common term (x+6). (x+6)(x-1) The factorization is (x+6)(x-1). 5. x^2 + 3x + 2 Step 1: Find two numbers that multiply to 2 and add up to 3. These numbers are 1 and 2. Step 2: Rewrite the middle term using these numbers. x^2 + x + 2x + 2 Step 3: Group terms and factor. x(x+1) + 2(x+1) Step 4: Factor out the common term (x+1). (x+1)(x+2) The factorization is (x+1)(x+2). Got more? Send 'em!