B) г) y(5x - y) + 4x(x – 3y). 136. Преобразуйте произведение в м a) (9 - a)(8 + a); б) (2b - 3c)(2c + 3b); Преобразуйте выражение в мно мощью формул сокращенного: 137. a) (a + 2)²; б) (3b - 1)²; в) (x 138. a) (4m + 5n)²; б) (2z - 3t)²; 139. a) (3x - 1)(3x + 1); б) (13m - 11n)(13m + 11n);

Задание 136: Преобразование произведения в многочлен

а)
The expression is:
$$ (9-a)(8+a) $$
This is a product of two binomials. We can expand this by using the distributive property (FOIL method):
First terms: $$ 9 \times 8 = 72 $$
Outer terms: $$ 9 \times a = 9a $$
Inner terms: $$ -a \times 8 = -8a $$
Last terms: $$ -a \times a = -a^2 $$
Combining these terms: $$ 72 + 9a - 8a - a^2 $$
Simplifying by combining like terms ($$ 9a - 8a = a $$): $$ 72 + a - a^2 $$
So, $$ (9-a)(8+a) = -a^2 + a + 72 $$

б)
The expression is:
$$ (2b - 3c)(2c + 3b) $$
Let's rearrange the second binomial so the terms are in the same order as the first: $$ (2b - 3c)(3b + 2c) $$
Now, we expand using the distributive property (FOIL):
First terms: $$ 2b \times 3b = 6b^2 $$
Outer terms: $$ 2b \times 2c = 4bc $$
Inner terms: $$ -3c \times 3b = -9bc $$
Last terms: $$ -3c \times 2c = -6c^2 $$
Combining these terms: $$ 6b^2 + 4bc - 9bc - 6c^2 $$
Simplifying by combining like terms ($$ 4bc - 9bc = -5bc $$): $$ 6b^2 - 5bc - 6c^2 $$
So, $$ (2b - 3c)(2c + 3b) = 6b^2 - 5bc - 6c^2 $$

Задание 137: Преобразование выражений с помощью формул сокращенного умножения

а)
The expression is:
$$ (a + 2)² $$
This is a square of a binomial, which follows the formula $$ (x + y)^2 = x^2 + 2xy + y^2 $$
Here, $$ x = a $$ and $$ y = 2 $$
Applying the formula: $$ a^2 + 2(a)(2) + 2^2 $$
Simplifying: $$ a^2 + 4a + 4 $$
So, $$ (a + 2)^2 = a^2 + 4a + 4 $$

б)
The expression is:
$$ (3b - 1)² $$
This is a square of a binomial, which follows the formula $$ (x - y)^2 = x^2 - 2xy + y^2 $$
Here, $$ x = 3b $$ and $$ y = 1 $$
Applying the formula: $$ (3b)^2 - 2(3b)(1) + 1^2 $$
Simplifying: $$ 9b^2 - 6b + 1 $$
So, $$ (3b - 1)^2 = 9b^2 - 6b + 1 $$

в)
(x
This question is incomplete as presented. The expression starts with '(x' but does not provide the full expression to be simplified.

Задание 138: Преобразование выражений с помощью формул сокращенного умножения

а)
The expression is:
$$ (4m + 5n)² $$
This is a square of a binomial, which follows the formula $$ (x + y)^2 = x^2 + 2xy + y^2 $$
Here, $$ x = 4m $$ and $$ y = 5n $$
Applying the formula: $$ (4m)^2 + 2(4m)(5n) + (5n)^2 $$
Simplifying: $$ 16m^2 + 40mn + 25n^2 $$
So, $$ (4m + 5n)^2 = 16m^2 + 40mn + 25n^2 $$

б)
The expression is:
$$ (2z - 3t)² $$
This is a square of a binomial, which follows the formula $$ (x - y)^2 = x^2 - 2xy + y^2 $$
Here, $$ x = 2z $$ and $$ y = 3t $$
Applying the formula: $$ (2z)^2 - 2(2z)(3t) + (3t)^2 $$
Simplifying: $$ 4z^2 - 12zt + 9t^2 $$
So, $$ (2z - 3t)^2 = 4z^2 - 12zt + 9t^2 $$

Задание 139: Преобразование выражения в многочлен

а)
The expression is:
$$ (3x - 1)(3x + 1) $$
This is a product of the sum and difference of two terms, which follows the formula $$ (x - y)(x + y) = x^2 - y^2 $$
Here, $$ x = 3x $$ and $$ y = 1 $$
Applying the formula: $$ (3x)^2 - 1^2 $$
Simplifying: $$ 9x^2 - 1 $$
So, $$ (3x - 1)(3x + 1) = 9x^2 - 1 $$

б)
The expression is:
$$ (13m - 11n)(13m + 11n) $$
This is a product of the sum and difference of two terms, which follows the formula $$ (x - y)(x + y) = x^2 - y^2 $$
Here, $$ x = 13m $$ and $$ y = 11n $$
Applying the formula: $$ (13m)^2 - (11n)^2 $$
Simplifying: $$ 169m^2 - 121n^2 $$
So, $$ (13m - 11n)(13m + 11n) = 169m^2 - 121n^2 $$