(2x+1)(x-5)-(4x+2)(3x+7)+(1+2x)
= 2x^2 - 10x + x - 5 -(12x^2 + 28x + 6x + 14) + 1+2x
= -10x^2 - 41x -18
Is that factorization?
no, what I did is called expanding.
(x+1)(x-2) = x^2 - x - 2 ------> expanding (take brackets away)
x^2 - x - 2 = (x+1)(x-2) ------> factoring (put brackets in)
To simplify the expression (2x+1)(x-5)-(4x+2)(3x+7)+(1+2x), we need to apply the distributive property and simplify each term separately. Let's break it down step by step:
1. Start by expanding the first term: (2x+1)(x-5).
Use the distributive property to multiply each term in the first set of parentheses by each term in the second set of parentheses:
(2x+1)(x-5) = 2x(x) + 2x(-5) + 1(x) + 1(-5)
= 2x^2 - 10x + x - 5
= 2x^2 - 9x - 5
2. Now, let's expand the second term: (4x+2)(3x+7).
Again, use the distributive property to multiply each term:
(4x+2)(3x+7) = 4x(3x) + 4x(7) + 2(3x) + 2(7)
= 12x^2 + 28x + 6x + 14
= 12x^2 + 34x + 14
3. Finally, let's simplify the third term: (1+2x).
This term doesn't require any further expansion since it is already simplified.
Now, we can substitute the results back into the original expression and combine like terms:
(2x+1)(x-5)-(4x+2)(3x+7)+(1+2x) = 2x^2 - 9x - 5 - (12x^2 + 34x + 14) + (1 + 2x)
Next, distribute the negative sign into the second term:
= 2x^2 - 9x - 5 - 12x^2 - 34x - 14 + 1 + 2x
Combine like terms:
= 2x^2 - 12x^2 - 9x - 34x + 2x - 5 - 14 + 1
= (2x^2 - 12x^2) + (-9x - 34x + 2x) + (-5 - 14 + 1)
= -10x^2 - 41x - 18
So, the simplified expression is -10x^2 - 41x - 18.