sovle: (3x - 2y)^2
The answer is 9x^2 + 4y^2 - 12xy but I do not know how to get the 12xy part.
20 - 4/5x is greater that or equal to 16, then:
The answer is x is less thatn or equal to 5 but again I do not know how to get this.
(3x - 2y)^2 = (3x-2y)(3x-2y)
You could use FOIL
(3x)(3x)+(3x)(-2y)+(-2y)(3x)+(-2y)(-2y)
= 9x^2 -12xy +4y^2
or use the distributive property of multipication directly
3x(3x-2y) - 2y(3x-2y)
=9 x^2 -6xy -6xy + 4y^2
= 9x^2 - 12 xy + 4y^2
20 - 4/5x >/= 16
If that is what you mean then
100 x - 4 >/= 80 x
20 x - 4 >/= 0
20 x >/= 4
x >/= 1/5
or if you mean
20 - (4/5)x >/= 16
20 - 16 >/= (4/5) x
4 >/= (4/5) x
5 >/= x
To solve the expression (3x - 2y)^2, we can use the formula for expanding a square of a binomial, which is:
(a - b)^2 = a^2 - 2ab + b^2
In this case, a = 3x and b = 2y. Substituting these values into the formula, we get:
(3x - 2y)^2 = (3x)^2 - 2(3x)(2y) + (2y)^2
= 9x^2 - 12xy + 4y^2
So the expression (3x - 2y)^2 expands to 9x^2 - 12xy + 4y^2.
Now, let's move on to the inequality 20 - (4/5)x ≥ 16. To solve this inequality, we'll isolate the variable x. Here's the step-by-step process:
1. Start by subtracting 20 from both sides of the inequality:
20 - (4/5)x - 20 ≥ 16 - 20
-(4/5)x ≥ -4
2. Now, multiply both sides of the inequality by -5/4 to get rid of the fraction and reverse the inequality sign (since we're multiplying/dividing by a negative number):
-(4/5)x * (-5/4) ≤ -4 * (-5/4)
x ≤ 5
As a result, we found that x is less than or equal to 5.
By following these steps, we obtained the solution x ≤ 5 for the given inequality.