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
kamogelo, let's knock this out. a) Step 1: Apply the exponent rule b^0 = 1. 3ab^0 × 2a^2b = 3a(1) × 2a^2b Step 2: Multiply the coefficients. 3 × 2 = 6 Step 3: Multiply the a terms using the rule a^m × a^n = a^m+n. a × a^2 = a^1+2 = a^3 Step 4: Multiply the b terms. 1 × b = b Step 5: Combine the results. 6a^3b The simplified expression is: 6a^3b b) Step 1: Distribute -x to each term inside the parentheses. -x(2x+7) = (-x)(2x) + (-x)(7) Step 2: Perform the multiplications. -2x^2 - 7x The simplified expression is: -2x^2 - 7x c) Step 1: Distribute 3x^2 to each term inside the parentheses. 3x^2(x^2+2) = (3x^2)(x^2) + (3x^2)(2) Step 2: Perform the multiplications using the rule x^m × x^n = x^m+n. 3x^2+2 + 6x^2 3x^4 + 6x^2 The simplified expression is: 3x^4 + 6x^2 d) Step 1: Distribute -5 to each term inside the parentheses. -5(2x-6y+4) = (-5)(2x) + (-5)(-6y) + (-5)(4) Step 2: Perform the multiplications. -10x + 30y - 20 The simplified expression is: -10x + 30y - 20 e) Step 1: Apply the exponent rule p^0 = 1 inside the parentheses. 7p(-2p^0+4p-1) = 7p(-2(1)+4p-1) 7p(-2+4p-1) Step 2: Distribute 7p to each term inside the parentheses. 7p(-2) + 7p(4p) + 7p(-1) Step 3: Perform the multiplications. -14p + 28p^2 - 7p Step 4: Combine like terms. 28p^2 + (-14p - 7p) 28p^2 - 21p The simplified expression is: 28p^2 - 21p f) Step 1: Distribute 4y to each term inside the parentheses. 4y(2y-3x+6) = (4y)(2y) + (4y)(-3x) + (4y)(6) Step 2: Perform the multiplications. 8y^2 - 12xy + 24y The simplified expression is: 8y^2 - 12xy + 24y g) Step 1: Distribute 3m into the first set of parentheses. 3m(-4m-3n) = (3m)(-4m) + (3m)(-3n) -12m^2 - 9mn Step 2: Distribute -2m into the second set of parentheses. -2m(-b+n) = (-2m)(-b) + (-2m)(n) 2mb - 2mn Step 3: Combine the results from Step 1 and Step 2. (-12m^2 - 9mn) - (2mb - 2mn) Step 4: Distribute the negative sign to the terms in the second parenthesis. -12m^2 - 9mn - 2mb + 2mn Step 5: Combine like terms (-9mn and 2mn). -12m^2 + (-9mn + 2mn) - 2mb -12m^2 - 7mn - 2mb The simplified expression is: -12m^2 - 7mn - 2mb h) Step 1: Distribute 4x into the first set of parentheses. 4x(x+2) = (4x)(x) + (4x)(2) 4x^2 + 8x Step 2: Distribute -3x into the second set of parentheses. -3x(x-4) = (-3x)(x) + (-3x)(-4) -3x^2 + 12x Step 3: Combine the results from Step 1 and Step 2. (4x^2 + 8x) + (-3x^2 + 12x) Step 4: Remove the parentheses. 4x^2 + 8x - 3x^2 + 12x Step 5: Combine like terms (4x^2 with -3x^2, and 8x with 12x). (4x^2 - 3x^2) + (8x + 12x) x^2 + 20x The simplified expression is: x^2 + 20x What's next?