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
Here are the simplified expressions: a) Step 1: Use the formula (a+b)^2 = a^2 + 2ab + b^2. Here, a=x and b=3. (x+3)^2 = x^2 + 2(x)(3) + 3^2 Step 2: Simplify the terms. = x^2 + 6x + 9 The simplified expression is x^2 + 6x + 9. b) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=x and b=3. (x-3)^2 = x^2 - 2(x)(3) + 3^2 Step 2: Simplify the terms. = x^2 - 6x + 9 The simplified expression is x^2 - 6x + 9. c) Step 1: Use the formula (a+b)^2 = a^2 + 2ab + b^2. Here, a=x and b=7. (x+7)^2 = x^2 + 2(x)(7) + 7^2 Step 2: Simplify the terms. = x^2 + 14x + 49 The simplified expression is x^2 + 14x + 49. d) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=x and b=1. (x-1)^2 = x^2 - 2(x)(1) + 1^2 Step 2: Simplify the terms. = x^2 - 2x + 1 The simplified expression is x^2 - 2x + 1. e) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=x and b=12. (x-12)^2 = x^2 - 2(x)(12) + 12^2 Step 2: Simplify the terms. = x^2 - 24x + 144 The simplified expression is x^2 - 24x + 144. f) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=x and b=9. (x-9)^2 = x^2 - 2(x)(9) + 9^2 Step 2: Simplify the terms. = x^2 - 18x + 81 The simplified expression is x^2 - 18x + 81. g) Step 1: Use the formula (a+b)^2 = a^2 + 2ab + b^2. Here, a=x and b=11. (x+11)^2 = x^2 + 2(x)(11) + 11^2 Step 2: Simplify the terms. = x^2 + 22x + 121 The simplified expression is x^2 + 22x + 121. h) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=2x and b=1. (2x-1)^2 = (2x)^2 - 2(2x)(1) + 1^2 Step 2: Simplify the terms. = 4x^2 - 4x + 1 The simplified expression is 4x^2 - 4x + 1. i) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=3x^3 and b=2y^2. (3x^3 - 2y^2)^2 = (3x^3)^2 - 2(3x^3)(2y^2) + (2y^2)^2 Step 2: Simplify the terms. = 9x^6 - 12x^3y^2 + 4y^4 The simplified expression is 9x^6 - 12x^3y^2 + 4y^4. j) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=9x^2 and b=m^8. (9x^2 - m^8)^2 = (9x^2)^2 - 2(9x^2)(m^8) + (m^8)^2 Step 2: Simplify the terms. = 81x^4 - 18x^2m^8 + m^16 The simplified expression is 81x^4 - 18x^2m^8 + m^16. k) Step 1: Use the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a=2p and b=q^2. (2p-q^2)^2 = (2p)^2 - 2(2p)(q^2) + (q^2)^2 Step 2: Simplify the terms. = 4p^2 - 4pq^2 + q^4 The simplified expression is 4p^2 - 4pq^2 + q^4. Send me the next one 📸