Question

1. Раскрыть скобки: а) ( x+3)^2 ; б) ( y - 8)^2 ; в) ( 7-x)^2-(5-x)^2; г) (4х+х) (х-4) ; д) ( 2-х) ( 4+х)2. Дана функция у= - 2x + 3. Найти значение функции, если значение аргумента равно 7,5.3. Упростите выражение:а) ( 2x - 5)^2+20xб) 36c - 3 (1+6c)^2

Answer 1

1. Х²+6х+9
У²-16у+64
(7-х-5+х)(7-х+5-x)=2(12-2x)=24-4x
5x(x-4)=5x²-20x
8-4x+2x-x²=-x²-2x+8

2. У=-2*7,5+3=-12

3. 2х²-20х+25+20х=2х²+25
36с-3(1+12с+36с²)=36с-3-36с-108с²=-3-108с²

Answer 2

1а)(х+3)²= Х²+6х+9
б)(у-8)²=У²-16у+64
в)(7-х)²-(5-х)²=(7-х-5+х)(7-х+5-x)=2(12-2x)=24-4x
г)(4х+х)(х-4)=5x(x-4)=5x²-20x
д)(2-х)(4+х)=8-4x+2x-x²=-x²-2x+8

2) у=-2х+3
х=7,5        -2*7,5+3=-12

3а)(2х-5)²+20х=4х²-20х+25+20х=4х²+25
б)36с-3(1+6с)²=36с-3-36с-108с²=-3-108с²

Answer 3

Раскрытие скобок:

a) (+x + 3)^2

To expand this expression, we can use the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2.

In this case, a = x and b = 3. Plugging these values into the formula, we get:

(+x + 3)^2 = x^2 + 2(x)(3) + 3^2 = x^2 + 6x + 9

b) (+y - 8)^2

Using the same formula, with a = y and b = -8:

(+y - 8)^2 = y^2 + 2(y)(-8) + (-8)^2 = y^2 - 16y + 64

в) (+7 - x)^2 - (5 - x)^2

We can expand each part separately:

(+7 - x)^2 = (7 - x)^2 = 7^2 - 2(7)(x) + x^2 = 49 - 14x + x^2

(5 - x)^2 = (5 - x)(5 - x) = 5^2 - 2(5)(x) + x^2 = 25 - 10x + x^2

Now, subtracting the second expression from the first:

(+7 - x)^2 - (5 - x)^2 = (49 - 14x + x^2) - (25 - 10x + x^2) = 49 - 14x + x^2 - 25 + 10x - x^2 = 24 - 4x

г) (4x + x) + (x - 4)

This expression can be simplified by combining like terms:

(4x + x) + (x - 4) = 5x + x + x - 4 = 7x - 4

д) (+2 - x) + (+4 + x)^2

Expanding the second part first:

(+4 + x)^2 = (4 + x)^2 = 4^2 + 2(4)(x) + x^2 = 16 + 8x + x^2

Now, adding the two expressions together:

(+2 - x) + (+4 + x)^2 = (2 - x) + (16 + 8x + x^2) = 2 - x + 16 + 8x + x^2 = x^2 + 7x + 18

Значение функции при аргументе 7,5:

Given the function u = -2x + 3, we need to find the value of the function when the argument is 7.5.

To do this, we can substitute the value of x into the function:

u = -2x + 3 u = -2(7.5) + 3 u = -15 + 3 u = -12

So, when x = 7.5, the value of the function is -12.

Упрощение выражения:

а) (+2x - 5)^2 + 20x

To simplify this expression, we can expand the squared term using the formula for squaring a binomial:

(+2x - 5)^2 = (2x - 5)^2 = (2x)^2 - 2(2x)(5) + 5^2 = 4x^2 - 20x + 25

Now, we can rewrite the expression:

(+2x - 5)^2 + 20x = 4x^2 - 20x + 25 + 20x = 4x^2 + 25

б) 36c - 3 + (1 + 6c)^2

Similarly, we can expand the squared term:

(1 + 6c)^2 = (1 + 6c)(1 + 6c) = 1^2 + 2(1)(6c) + (6c)^2 = 1 + 12c + 36c^2

Now, we can rewrite the expression:

36c - 3 + (1 + 6c)^2 = 36c - 3 + 1 + 12c + 36c^2 = 36c + 12c + 36c^2 - 3 + 1 = 48c + 36c^2 - 2

So, the simplified expression is 48c + 36c^2 - 2.