Question

31.3 РАЗЛОЖиТЬ НА НОЖИТЕЛИ РЕШИТЬ: 1)A^2-49; 8)T^2-400/4412)64-B^2; 9)25*x^2-363)C^2-2,25; 10)-16+49*y^24)2,89-D^2; 11)0,64-1/9*z^25)64/81-X^2; 12)4/25*t^2-366)100/121-Y^2;7)Z^2-169/196;

Answer 1

1) (a+7)(a -7)

2) (8+b) (8-b)

3) (c + 1.5)(c - 1.5)

4) (1.7+d) (1.7-d)

5) (8/9+x) (8/9-x)

6) (10/11+y) (10/11-y)

7) (z + 13/14)(z -13/14)

8) (t +20/21)(t -20/21)

9) (5x +6)(5x-6)

10) (7y +4)(7y-4)

11) (0.8+1/3z)(0.8-1/3z)

12) (2/5t+6)(2/5t-6)

Answer 2

To factorize the given expressions, let's work through each one:

1. A^2 - 49: This is a difference of squares, so we can apply the identity (a^2 - b^2) = (a + b)(a - b). Therefore, A^2 - 49 can be factorized as (A + 7)(A - 7).

2. 64 - B^2: Similar to the previous expression, this is a difference of squares. So we can factorize it as (8 + B)(8 - B).

3. 25*x^2 - 36: This expression cannot be factored further since it is a difference of squares and there are no perfect square factors.

4. 2.89 - D^2: Again, this is a difference of squares. So we can factorize it as (√2.89 + D)(√2.89 - D).

5. 64/81 - X^2: This is another difference of squares. So we can factorize it as (√(64/81) + X)(√(64/81) - X). Simplifying the square root, we get (√(64)/√(81) + X)(√(64)/√(81) - X). Since √64 = 8 and √81 = 9, the factorization is (8/9 + X)(8/9 - X).

6. 100/121 - Y^2: This expression can be factored as (√(100/121) + Y)(√(100/121) - Y). Simplifying the square root, we get (√(100)/√(121) + Y)(√(100)/√(121) - Y). Since √100 = 10 and √121 = 11, the factorization is (10/11 + Y)(10/11 - Y).

7. Z^2 - 169/196: This is another difference of squares. So we can factorize it as (Z + √(169/196))(Z - √(169/196)). Simplifying the square root, we get (Z + 13/14)(Z - 13/14).

8. T^2 - 400/441: This expression can be factorized as (T + √(400/441))(T - √(400/441)). Simplifying the square root, we get (T + 20/21)(T - 20/21).

9. 4/25 * t^2 - 36: This expression can be factorized as (2/5 * t + 6)(2/5 * t - 6).

10. -16 + 49 * y^2: This is a difference of squares. So we can factorize it as (7y + 4)(7y - 4).

11. 0.64 - 1/9 * z^2: This is another difference of squares. So we can factorize it as (√0.64 + 1/3z)(√0.64 - 1/3z). Simplifying the square root, we get (0.8 + 1/3z)(0.8 - 1/3z).

Please note that the expressions have been factorized as much as possible based on the given information.