develop the products and simplify 3x (x + 2) - (4x + 1) (5x − 3)
3x (x + 2) - (4x + 1) (5x − 3)
3x^2 + 6x - (20x^2 - 7x - 3)
-17x^2 + 13x + 3
4a^2-a(b+2)(b-a)
4a^2 - a(b^2+2b-2a-ab)
4a^2 - ab^2 - 2ab + 2a^2 + a^2b
6a^2 + a^2b - 2ab - ab^2
Note that ab^2 ≠ a^2b
I been trying to wrap my head around examples.
For example another question 4a2-a(b+2)(b-a)
Would it become
=4a2-ab2+a2b-2ab+2a2
=6a2-2ab
?
I assume -a * 1ab gives me a^2b. I understand the rest, but why does that occur there? I guess it's simplified too?
Another example to make sure I get this (x − 5) (5 − x) +25
=5x - x^2 -25 + 5x + 25
=10x - x^2 ?
To develop the products and simplify the given expression, we will use the distributive property and combine like terms. Here are the steps:
Step 1: Expand the expression using the distributive property.
3x * (x + 2) = 3x * x + 3x * 2 = 3x^2 + 6x
-(4x + 1) * (5x - 3) = -4x * (5x - 3) - 1 * (5x - 3) = -20x^2 + 12x + 5x - 3 = -20x^2 + 17x - 3
Step 2: Combine like terms.
Combine the terms that have the same variable and exponent:
(3x^2 + 6x) - (20x^2 + 17x - 3) = 3x^2 + 6x - 20x^2 - 17x + 3
Step 3: Simplify the expression by combining like terms further.
Combine the like terms:
(3x^2 - 20x^2) + (6x - 17x) + 3 = -17x^2 - 11x + 3
The simplified expression for 3x(x + 2) - (4x + 1)(5x − 3) is -17x^2 - 11x + 3.