Question

Расскрыть скобки по образцу Образец:(a+b)^2=(a+b)(a+b)=a^2+ab+ab+b^2=a^2+2ab+b^2 1)(2a-3b)(2b-3a) 2)(5x-3y)^2 3)(10c+d)^3 4)(5a+3x)(2a-x)(3x-2a) 5)(2e-3)(10+3e) Пожалуйста с решением(с ходом мыслей)

Answer 1

Решение смотри в приложении

Answer 2

Solution:

Let's expand each expression step by step:

1. (a+b)^2 = a^2 + 2ab + b^2 - This is the formula for squaring a binomial expression. - The square of a binomial expression is equal to the square of the first term plus twice the product of the two terms plus the square of the second term. - In this case, the expression is (a+b), so the square is equal to a^2 + 2ab + b^2.

2. (2a-3b)(2b-3a) - To expand this expression, we can use the FOIL method, which stands for First, Outer, Inner, Last. - Multiply the first terms, the outer terms, the inner terms, and the last terms, and then combine like terms. - Applying the FOIL method, we get: 4ab - 6a^2 - 6b^2 + 9ab. - Simplifying further, we have: 13ab - 6a^2 - 6b^2.

3. (5x-3y)^2 - Similar to the first example, we can square the binomial expression (5x-3y). - Using the formula for squaring a binomial, we get: (5x)^2 - 2(5x)(3y) + (3y)^2. - Simplifying, we have: 25x^2 - 30xy + 9y^2.

4. (10c+d)^3 - To expand this expression, we can use the binomial theorem, which states that (a+b)^n can be expanded as the sum of the terms: C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + ... + C(n,n-1)ab^(n-1) + C(n,n)b^n, where C(n,k) represents the binomial coefficient. - Applying the binomial theorem to (10c+d)^3, we get: C(3,0)(10c)^3 + C(3,1)(10c)^2(d) + C(3,2)(10c)(d)^2 + C(3,3)(d)^3. - Simplifying, we have: 1000c^3 + 3000c^2d + 3000cd^2 + d^3.

5. (5a+3x)(2a-x)(3x-2a) - To expand this expression, we can use the distributive property and multiply each term of the first expression by each term of the second and third expressions. - Expanding step by step, we get: (5a)(2a)(3x) + (5a)(2a)(-2a) + (5a)(-x)(3x) + (5a)(-x)(-2a) + (3x)(2a)(3x) + (3x)(2a)(-2a) + (3x)(-x)(3x) + (3x)(-x)(-2a). - Simplifying, we have: 30a^2x^2 - 20a^3x - 15ax^3 + 10a^2x^2 + 18a^2x^2 - 12a^3x - 9x^4 + 6a^2x^2. - Combining like terms, we get: 64a^2x^2 - 32a^3x - 9x^4 - 15ax^3.

6. (2e-3)(10+3e) - To expand this expression, we can use the distributive property and multiply each term of the first expression by each term of the second expression. - Expanding step by step, we get: (2e)(10) + (2e)(3e) + (-3)(10) + (-3)(3e). - Simplifying, we have: 20e + 6e^2 - 30 - 9e. - Combining like terms, we get: 6e^2 + 11e - 30.

Therefore, the expanded forms of the given expressions are: 1. (a+b)^2 = a^2 + 2ab + b^2 2. (2a-3b)(2b-3a) = 13ab - 6a^2 - 6b^2 3. (5x-3y)^2 = 25x^2 - 30xy + 9y^2 4. (10c+d)^3 = 1000c^3 + 3000c^2d + 3000cd^2 + d^3 5. (5a+3x)(2a-x)(3x-2a) = 64a^2x^2 - 32a^3x - 9x^4 - 15ax^3 6. (2e-3)(10+3e) = 6e^2 + 11e - 30

I hope this helps! Let me know if you have any further questions.