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.
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Here are the simplified expressions: Classwork: Simplify the following multiplication 1) 2x × x^2 Step 1: Multiply the coefficients and add the exponents of the variables. 2x × x^2 = 2 · x^1+2 = 2x^3 The simplified expression is 2x^3. 2) 4y^3 × 3y Step 1: Multiply the coefficients. 4y^3 × 3y = (4 × 3) · (y^3 × y^1) Step 2: Add the exponents of the variable y. = 12y^3+1 = 12y^4 The simplified expression is 12y^4. 3) 2a^2 × 3a Step 1: Multiply the coefficients. 2a^2 × 3a = (2 × 3) · (a^2 × a^1) Step 2: Add the exponents of the variable a. = 6a^2+1 = 6a^3 The simplified expression is 6a^3. 4) 3b × 5b Step 1: Multiply the coefficients. 3b × 5b = (3 × 5) · (b^1 × b^1) Step 2: Add the exponents of the variable b. = 15b^1+1 = 15b^2 The simplified expression is 15b^2. 5) 6x^2 × 7x^3 Step 1: Multiply the coefficients. 6x^2 × 7x^3 = (6 × 7) · (x^2 × x^3) Step 2: Add the exponents of the variable x. = 42x^2+3 = 42x^5 The simplified expression is 42x^5. Classwork: Simplify the following 1) 3(x-y) Step 1: Distribute the 3 to each term inside the parentheses. 3(x-y) = 3 × x - 3 × y = 3x - 3y The simplified expression is 3x - 3y. 2) 4(m+1) Step 1: Distribute the 4 to each term inside the parentheses. 4(m+1) = 4 × m + 4 × 1 = 4m + 4 The simplified expression is 4m + 4. 3) 2(2a+3b) Step 1: Distribute the 2 to each term inside the parentheses. 2(2a+3b) = 2 × 2a + 2 × 3b = 4a + 6b The simplified expression is 4a + 6b. 4) 5(c-4) Step 1: Distribute the 5 to each term inside the parentheses. 5(c-4) = 5 × c - 5 × 4 = 5c - 20 The simplified expression is 5c - 20. 5) 6(2x+3-1) Step 1: Simplify the terms inside the parentheses first. 6(2x+3-1) = 6(2x+2) Step 2: Distribute the 6 to each term inside the parentheses. = 6 × 2x + 6 × 2 = 12x + 12 The simplified expression is 12x + 12. That's 2 down. 3 left today — send the next one.