Question

A(3a+2b)-b(2a-5b) - упростить (x-2)²+3x-6-5(2-x)=0 - решить 5ay-3bx+ax-15by - разложить на множители

Answer 1

a(3a+2b)-b(2a-5b)

3a²+2ab-2ab+5b²

3a²+5b²

(x-2)²+3x-6-5(2-x)=0

x²-4x+4+3x-6-10+5x=0

x²+4x-12=0

D=4²-4*1(-12)=16-(-48)=16+48=64=8²

x1=(-4-8)/(2*1)=-12/2=-6

x2=(-4+8)/(2*1)=4/2=2

Ответ:x1=-6;x2=2

5ay-3bx+ax-15by

5ay-15by+ax-3bx

5y(a-3b)+x(a-3b)

(5y+x)(a-3b)

Answer 2

Let's take each question step by step:

1. Simplify the expression A(3a+2b) - b(2a-5b): To simplify, we will perform the distribution and combine like terms:

A(3a+2b) - b(2a-5b)
= 3aA + 2bA - 2ab + 5b^2

2. Solve the equation (x-2)² + 3x - 6 - 5(2-x) = 0: To solve the equation, first expand and simplify the left side:

(x-2)² + 3x - 6 - 5(2-x) = 0
(x-2)(x-2) + 3x - 6 - 10 + 5x = 0
(x^2 - 4x + 4) + 3x - 16 = 0
x^2 - 4x + 3x - 12 = 0
x^2 - x - 12 = 0

Now, let's factor the quadratic equation:

(x - 4)(x + 3) = 0

Now, set each factor to zero and solve for x:

x - 4 = 0 => x = 4 x + 3 = 0 => x = -3

So the solutions to the equation are x = 4 and x = -3.

3. Factor the expression 5ay - 3bx + ax - 15by: To factor the expression, we'll look for common terms in each pair of terms:

5ay - 3bx + ax - 15by

Group the terms:

(5ay + ax) + (-3bx - 15by)

Factor out common terms from each group:

a(5y + x) + (-3b)(x + 5y)

The factored form of the expression is: a(5y + x) - 3b(x + 5y).