Question

3a(2a+7)-(2a+1)(3a-4) 3m(1-6m)-(2m-1)(2m+1) 5(a-b)+(a+b)(a-b)-a^2

Answer 1

3a(2a+7)-(2a+1)(3a-4)=6а^2 +21а-6а^2 +8а-3а+4=26а+4

3m(1-6m)-(2m-1)(2m+1)=3m-18m^2 - 4m^2 - 2m+2m+1=-22m^2 +3m+1

5(a-b)+(a+b)(a-b)-a^2=5a-5b+a^2 - b^2 - a^2 =5a-5b-b^2

Answer 2

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Answer 3

To simplify the given expression, let's break it down step by step:

1. Simplify the expression within each set of parentheses first: - For the expression 3a(2a + 7), we distribute 3a to each term inside the parentheses: 6a^2 + 21a. - For the expression (2a + 1)(3a - 4), we use the FOIL method (First, Outer, Inner, Last) to multiply the terms: - First: 2a * 3a = 6a^2 - Outer: 2a * -4 = -8a - Inner: 1 * 3a = 3a - Last: 1 * -4 = -4 - Combining these terms, we get 6a^2 - 8a + 3a - 4 = 6a^2 - 5a - 4.

2. Continue simplifying the remaining expressions: - For the expression 3m(1 - 6m), we distribute 3m to each term inside the parentheses: 3m - 18m^2. - For the expression (2m - 1)(2m + 1), again using the FOIL method: - First: 2m * 2m = 4m^2 - Outer: 2m * 1 = 2m - Inner: -1 * 2m = -2m - Last: -1 * 1 = -1 - Combining these terms, we get 4m^2 + 2m - 2m - 1 = 4m^2 - 1.

3. Now let's simplify the expression involving (a - b): - For the expression (a - b)(a + b), again using the FOIL method: - First: a * a = a^2 - Outer: a * b = ab - Inner: -b * a = -ab - Last: -b * b = -b^2 - Combining these terms, we get a^2 + ab - ab - b^2 = a^2 - b^2.

4. Finally, combine all the simplified terms: - The simplified expression becomes: 6a^2 + 21a - (6a^2 - 5a - 4) + 3m - 18m^2 - (4m^2 - 1) + 5(a - b) + (a^2 - b^2) - a^2.

Now let's combine like terms:

- Combining the terms with like variables: - 6a^2 - 6a^2 + 21a + 5a = 26a. - -18m^2 + 4m^2 + 3m = -14m^2 + 3m. - -b^2 + a^2.

- Combining the constant terms: - -4 - (-1) = -4 + 1 = -3.

Putting it all together, the simplified expression is: - 26a + (-14m^2 + 3m) + 5(a - b) + (a^2 - b^2) - 3.

The final simplified expression is: a^2 - b^2 - 14m^2 + 3m + 26a + 5(a - b) - 3.