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
Another one kamogelo — let's solve it. a) Simplify (a+2)(a+7). Step 1: Use the FOIL method (First, Outer, Inner, Last) to multiply the binomials. (a+2)(a+7) = a · a + a · 7 + 2 · a + 2 · 7 Step 2: Perform the multiplications. a^2 + 7a + 2a + 14 Step 3: Combine like terms. a^2 + 9a + 14 The simplified expression is a^2 + 9a + 14. b) Simplify (a+4)(a-6). (Assuming the second bracket is (a-6) based on the image clarity.) Step 1: Use the FOIL method to multiply the binomials. (a+4)(a-6) = a · a + a · (-6) + 4 · a + 4 · (-6) Step 2: Perform the multiplications. a^2 - 6a + 4a - 24 Step 3: Combine like terms. a^2 - 2a - 24 The simplified expression is a^2 - 2a - 24. c) Simplify (x-3)(x-9). Step 1: Use the FOIL method to multiply the binomials. (x-3)(x-9) = x · x + x · (-9) + (-3) · x + (-3) · (-9) Step 2: Perform the multiplications. x^2 - 9x - 3x + 27 Step 3: Combine like terms. x^2 - 12x + 27 The simplified expression is x^2 - 12x + 27. d) Simplify (m+5)(m-5). Step 1: Recognize this as a difference of squares pattern, (A+B)(A-B) = A^2 - B^2. (m+5)(m-5) = m^2 - 5^2 Step 2: Calculate the square. m^2 - 25 The simplified expression is m^2 - 25. e) Simplify (y-7)(y+7). Step 1: Recognize this as a difference of squares pattern, (A-B)(A+B) = A^2 - B^2. (y-7)(y+7) = y^2 - 7^2 Step 2: Calculate the square. y^2 - 49 The simplified expression is y^2 - 49. f) Simplify (2a+7)^2. Step 1: Use the square of a binomial formula, (A+B)^2 = A^2 + 2AB + B^2. (2a+7)^2 = (2a)^2 + 2(2a)(7) + 7^2 Step 2: Perform the multiplications and squaring. 4a^2 + 28a + 49 The simplified expression is 4a^2 + 28a + 49. g) Simplify (2x^2-8)^2. Step 1: Use the square of a binomial formula, (A-B)^2 = A^2 - 2AB + B^2. (2x^2-8)^2 = (2x^2)^2 - 2(2x^2)(8) + 8^2 Step 2: Perform the multiplications and squaring. 4x^4 - 32x^2 + 64 The simplified expression is 4x^4 - 32x^2 + 64. h) Simplify -2(x-3)^2 - 3(x+1)(2x-5). Step 1: Expand (x-3)^2. (x-3)^2 = x^2 - 2(x)(3) + 3^2 = x^2 - 6x + 9 Step 2: Expand (x+1)(2x-5). (x+1)(2x-5) = x(2x) + x(-5) + 1(2x) + 1(-5) = 2x^2 - 5x + 2x - 5 = 2x^2 - 3x - 5 Step 3: Substitute the expanded forms back into the original expression. -2(x^2 - 6x + 9) - 3(2x^2 - 3x - 5) Step 4: Distribute the constants. -2x^2 + 12x - 18 - 6x^2 + 9x + 15 Step 5: Combine like terms. (-2x^2 - 6x^2) + (12x + 9x) + (-18 + 15) -8x^2 + 21x - 3 The simplified expression is -8x^2 + 21x - 3. i) Simplify -2(m-4)^2 - 3m - (m+6)(m-6). Step 1: Expand (m-4)^2. (m-4)^2 = m^2 - 2(m)(4) + 4^2 = m^2 - 8m + 16 Step 2: Expand (m+6)(m-6) using the difference of squares formula. (m+6)(m-6) = m^2 - 6^2 = m^2 - 36 Step 3: Substitute the expanded forms back into the original expression. -2(m^2 - 8m + 16) - 3m - (m^2 - 36) Step 4: Distribute the constants and the negative sign. -2m^2 + 16m - 32 - 3m - m^2 + 36 Step 5: Combine like terms. (-2m^2 - m^2) + (16m - 3m) + (-32 + 36) -3m^2 + 13m + 4 The simplified expression is -3m^2 + 13m + 4. Send me the next one 📸