Question

Применить формулы сокращенного умножения: 1+x^2-2x; (2x-1)(2x+1); (k+0.5)^2; 28xy+49x^2+4y^2; (7x-2)(7x+2); (-a-1)^2; (b+3)^2; 25b^2+10b+1; (2a-3b)(2a+3b); b^2 -4/9 ; (10-c)^2; 81a^2-18ab+b^2; (5x^2+2y^3)(5x^2-2y^3); -49a^2+16b^2; (-b-3)^2; (0.3-m)^2; 8ab+b^2+16a^2; (4+y^2)(y^-4); (y+9)^2

Answer 1

1+х^2-2х=(х-1)^2

(2х-1)(2х+1)=4х^2-1

(к+0.5)^2=к^2+к+0.25

28ху+49х^2+4у^2=(2у+7х)^2

(7х-2)(7х+2)=49х^2-4

(-а-1)^2=а^2+2а+1

(б+3)^2=б^2+6б+9

25б^2+10б+1=(5б+1)^2

(2а-3б)(2а+3б)=4а^2+9б^2

б^2-4/9=(б-2/3)(б+2/3)

(10-с)^2=100-20с+с^2

81а^2-18аб+б^2=(9а-б)^2

(5х^2+2у^3)(5х^2-2у^3)=25х^4-4у^6

-49а^2+16б^2=(4б-7а)(4б+7а)

(-б-3)^2=б^2+6б+9

(0.3-м)^2=0.09-0.6м+м^2

8аб+б^2+16а^2=(4а+б)^2

(4+у^2)(у^2-4)=у^4-16

(у+9)^2=у^2+18у+81

Answer 2

To apply the formulas of the shortened multiplication, we can simplify each expression step by step:

1. 1 + x^2 - 2x: - There is no shortened multiplication in this expression. It is already simplified.

2. (2x - 1)(2x + 1): - This expression represents the difference of squares, which can be simplified using the formula (a - b)(a + b) = a^2 - b^2. - Applying the formula, we get (2x)^2 - 1^2 = 4x^2 - 1.

3. (k + 0.5)^2: - This expression represents the square of a binomial, which can be simplified using the formula (a + b)^2 = a^2 + 2ab + b^2. - Applying the formula, we get k^2 + 2(0.5)(k) + (0.5)^2 = k^2 + k + 0.25.

4. 28xy + 49x^2 + 4y^2: - This expression cannot be simplified further using the formulas of shortened multiplication. It is already in its simplest form.

5. (7x - 2)(7x + 2): - This expression represents the difference of squares, which can be simplified using the formula (a - b)(a + b) = a^2 - b^2. - Applying the formula, we get (7x)^2 - 2^2 = 49x^2 - 4.

6. (-a - 1)^2: - This expression represents the square of a binomial, which can be simplified using the formula (a + b)^2 = a^2 + 2ab + b^2. - Applying the formula, we get (-a)^2 + 2(-a)(-1) + (-1)^2 = a^2 + 2a + 1.

7. (b + 3)^2: - This expression represents the square of a binomial, which can be simplified using the formula (a + b)^2 = a^2 + 2ab + b^2. - Applying the formula, we get b^2 + 2(b)(3) + 3^2 = b^2 + 6b + 9.

8. 25b^2 + 10b + 1: - This expression cannot be simplified further using the formulas of shortened multiplication. It is already in its simplest form.

9. (2a - 3b)(2a + 3b): - This expression represents the difference of squares, which can be simplified using the formula (a - b)(a + b) = a^2 - b^2. - Applying the formula, we get (2a)^2 - (3b)^2 = 4a^2 - 9b^2.

10. b^2 - 4/9: - This expression cannot be simplified further using the formulas of shortened multiplication. It is already in its simplest form.

11. (10 - c)^2: - This expression represents the square of a binomial, which can be simplified using the formula (a + b)^2 = a^2 + 2ab + b^2. - Applying the formula, we get 10^2 - 2(10)(c) + c^2 = 100 - 20c + c^2.

12. 81a^2 - 18ab + b^2: - This expression cannot be simplified further using the formulas of shortened multiplication. It is already in its simplest form.

13. (5x^2 + 2y^3)(5x^2 - 2y^3): - This expression represents the difference of squares, which can be simplified using the formula (a - b)(a + b) = a^2 - b^2. - Applying the formula, we get (5x^2)^2 - (2y^3)^2 = 25x^4 - 4y^6.

14. -49a^2 + 16b^2: - This expression cannot be simplified further using the formulas of shortened multiplication. It is already in its simplest form.

15. (-b - 3)^2: - This expression represents the square of a binomial, which can be simplified using the formula (a + b)^2 = a^2 + 2ab + b^2. - Applying the formula, we get (-b)^2 + 2(-b)(-3) + (-3)^2 = b^2 + 6b + 9.

16. (0.3 - m)^2: - This expression represents the square of a binomial, which can be simplified using the formula (a + b)^2 = a^2 + 2ab + b^2. - Applying the formula, we get (0.3)^2 - 2(0.3)(m) + m^2 = 0.09 - 0.6m + m^2.

17. 8ab + b^2 + 16a^2: - This expression cannot be simplified further using the formulas of shortened multiplication. It is already in its simplest form.

18. (4 + y^2)(y^-4): - This expression cannot be simplified further using the formulas of shortened multiplication. It