Question

Упростите выражение: 1) a) (3a + 5)(3a - 6) + 30;б) 3b2 + (8 - 3b) (b + 5);2) a) 8. x- (3x+ 1)(5x+ 1);б) 8p - (3p + 8)(2p - 5);3) a) (x- 3) (x + 5)- (x2 + x);b) a (a - 3) + (a + 1) (a + 4);б) (у + 2) (y + 3) - y (y - 1); r) (c + 2) c - (c + 3) (c - 3).2. При каком значении х равны значения следующихвыражений:a) (3.x+5)(4.x-1) и (6х- 3)(2x+7);б) (5.х - 1)(2 - x) и (x - 3)(2 - 5x)?​

Answer 1

1) 3 × (8 + b) = 3 × 8 + 3 × b = 24 + 3b;

2) 8 × (x - 7) = 8 × x - 8 × 7 = 8x - 56;

3) (8 - m) × 15 = 8 × 15 - m × 15 = 120 - 15m;

4) 22 × (7x + 4) = 22 × 7x + 22 × 4 = 154x + 88;

5) 7 × (3m + 9n - 18p) = 7 × 3m + 7 × 9n - 7 × 18p = 21m + 63n - 126p;

6) (2a - 5b + 3c) × 12 = 12 × 2a - 12 × 5b + 12 × 3c = 24a - 60b + 36c.

Answer 2

1. a) (3a + 5)(3a - 6) + 30:

To simplify this expression, we can use the distributive property and combine like terms.

(3a + 5)(3a - 6) + 30 = 9a^2 - 18a + 15a - 30 + 30 = 9a^2 - 3a

b) 3b^2 + (8 - 3b)(b + 5):

Using the distributive property and simplifying:

3b^2 + (8 - 3b)(b + 5) = 3b^2 + (8b + 40 - 3b^2 - 15b) = 8b - 12b^2 + 40

2. a) 8x - (3x + 1)(5x + 1):

Expanding and simplifying:

8x - (3x + 1)(5x + 1) = 8x - (15x^2 + 8x + 3x + 1) = 8x - 15x^2 - 11x - 1

b) 8p - (3p + 8)(2p - 5):

Expanding and simplifying:

8p - (3p + 8)(2p - 5) = 8p - (6p^2 - 15p + 16p - 40) = 8p - 6p^2 + 29p - 40

3. a) (x - 3)(x + 5) - (x^2 + x):

Expanding and simplifying:

(x - 3)(x + 5) - (x^2 + x) = x^2 + 5x - 3x - 15 - x^2 - x = 4x - 16

b) a(a - 3) + (a + 1)(a + 4):

Expanding and simplifying:

a(a - 3) + (a + 1)(a + 4) = a^2 - 3a + a^2 + 5a + 4 = 2a^2 + 2a + 4

(y + 2)(y + 3) - y(y - 1):

Expanding and simplifying:

(y + 2)(y + 3) - y(y - 1) = y^2 + 3y + 2y + 6 - y^2 + y = 6y + 6

(c + 2)c - (c + 3)(c - 3):

Expanding and simplifying:

(c + 2)c - (c + 3)(c - 3) = c^2 + 2c - (c^2 - 9) = c^2 + 2c - c^2 + 9 = 2c + 9

2. a) (3x + 5)(4x - 1) and (6x - 3)(2x + 7):

To find when these two expressions are equal, we can set them equal to each other and solve for x.

(3x + 5)(4x - 1) = (6x - 3)(2x + 7)

Expanding both sides:

12x^2 - 3x + 20x - 5 = 12x^2 + 42x - 6x - 21

Combining like terms:

12x^2 + 17x - 5 = 12x^2 + 36x - 21

Subtracting 12x^2 from both sides:

17x - 5 = 36x - 21

Subtracting 17x from both sides:

-5 = 19x - 21

Adding 21 to both sides:

16 = 19x

Dividing by 19:

x = 16/19

b) (5x - 1)(2 - x) and (x - 3)(2 - 5x):

Setting the expressions equal to each other:

(5x - 1)(2 - x) = (x - 3)(2 - 5x)

Expanding both sides:

10x - 5x^2 - 2 + x = 2x - 6 - 5x^2 + 15x

Combining like terms:

11x - 5x^2 - 2 + x = 17x - 5x^2

Rearranging terms:

-4x + 2 = 6x

Adding 4x to both sides:

2 = 10x

Dividing by 10:

x = 2/10

Simplifying further:

x = 1/5