expand and simplify:2(x+2)squared-(2x-1)(x+2) 2x(x-2)+5x(x÷3)-x(3x-1) (5x-3)(2xsquared+3x-3) solve for x:(x-2)squared+3x-2=(x+3)squared
I'm having a hard time parsing your text. Is it all one expression? What is the significance of the spaces? Or are there three separate expressions?
2(x+2)^2-(2x-1)(x+2) 2x(x-2)+5x(x/3)-x(3x-1) (5x-3)(2x^2+3x-3)
As for the other one, I think it's
(x-2)^2+3x-2 = (x+3)^2
well, you start out by expanding stuff and collecting like powers:
x^2-4x+4+3x-2 = x^2+6x+9
x^2-x+2 = =x^2+6x+9
7x = -7
x = -1
To expand and simplify the expression 2(x+2)^2 - (2x-1)(x+2), follow these steps:
Step 1: Expand the expression (x+2)^2:
(x+2)^2 = (x+2)(x+2) = x(x+2) + 2(x+2) = x^2 + 2x + 2x + 4 = x^2 + 4x + 4.
Step 2: Expand the expression (2x-1)(x+2) using the distributive property:
(2x-1)(x+2) = 2x(x+2) - 1(x+2) = 2x^2 + 4x - x - 2 = 2x^2 + 3x - 2.
Now, plug these values back into the original expression:
2(x+2)^2 - (2x-1)(x+2) = 2(x^2 + 4x + 4) - (2x^2 + 3x - 2)
= 2x^2 + 8x + 8 - 2x^2 - 3x + 2
= -x + 10.
So, the expanded and simplified expression is -x + 10.
Now, let's simplify the expression 2x(x-2) + 5x(x/3) - x(3x-1):
Step 1: Expand each term before combining like terms:
2x(x-2) = 2x^2 - 4x,
5x(x/3) = (5/3)x^2,
x(3x-1) = 3x^2 - x.
Step 2: Combine like terms:
2x^2 - 4x + (5/3)x^2 - (3x^2 - x)
= 2x^2 - 4x + (5/3)x^2 - 3x^2 + x
= -x^2 - 3x.
So, the simplified expression is -x^2 - 3x.
To expand and simplify the expression (5x-3)(2x^2+3x-3), follow these steps:
Step 1: Apply the distributive property:
(5x-3)(2x^2+3x-3) = 5x(2x^2+3x-3) - 3(2x^2+3x-3)
= 10x^3 + 15x^2 -15x - 6x^2 - 9x + 9
= 10x^3 + 9x^2 - 24x + 9.
So, the expanded and simplified expression is 10x^3 + 9x^2 - 24x + 9.
To solve the equation (x-2)^2 + 3x - 2 = (x+3)^2 for x, follow these steps:
Step 1: Expand both sides of the equation:
(x-2)^2 + 3x - 2 = (x^2 - 4x + 4) + 3x - 2 = x^2 - 4x + 4 + 3x - 2 = x^2 - x + 2.
Step 2: Simplify the equation:
x^2 - x + 2 = x^2 + 6x + 9.
Step 3: Combine like terms:
x^2 - x + 2 - x^2 - 6x - 9 = 0.
Step 4: Simplify the equation further:
-7x - 7 = 0.
Step 5: Add 7 to both sides to isolate x:
-7x - 7 + 7 = 0 + 7.
Step 6: Simplify:
-7x = 7.
Step 7: Divide both sides by -7 to solve for x:
-7x / -7 = 7 / -7.
Step 8: Simplify:
x = -1.
Therefore, the solution to the equation is x = -1.