Algebraic factorization

(2x-5)(3x+2)-(4x-10)(5x+4)

factor out a 2:

=(2x-5)(3x+2)-(2x-5)(2)(5x+4)
factor out (2x-5):
=(2x-5)[(3x+2)-2(5x+4)]
simplify:
=(2x-5)(3x+2-10x-8)
=(2x-5)(-7x-6)
and, if you want:
=-14x^2+23x+30

To factorize the given expression [(2x-5)(3x+2)] - [(4x-10)(5x+4)], we can use the distributive property to expand each of the products, and then combine like terms. Here are the step-by-step instructions:

Step 1: Expand the first product (2x - 5) * (3x + 2):
(2x - 5) * (3x + 2) = 2x * 3x + 2x * 2 + (-5) * 3x + (-5) * 2
= 6x^2 + 4x - 15x - 10
= 6x^2 - 11x - 10

Step 2: Expand the second product (4x - 10) * (5x + 4):
(4x - 10) * (5x + 4) = 4x * 5x + 4x * 4 + (-10) * 5x + (-10) * 4
= 20x^2 + 16x - 50x - 40
= 20x^2 - 34x - 40

Step 3: Subtract the second expression from the first expression:
(6x^2 - 11x - 10) - (20x^2 - 34x - 40)
= 6x^2 - 11x - 10 - 20x^2 + 34x + 40
= (6x^2 - 20x^2) + (-11x + 34x) + (-10 + 40)
= -14x^2 + 23x + 30

Therefore, the factorization of the expression (2x-5)(3x+2)-(4x-10)(5x+4) is -14x^2 + 23x + 30.

To solve the algebraic expression you provided, we need to multiply the terms inside each set of parentheses and then subtract the results.

Let's start by multiplying the terms inside the first set of parentheses, (2x - 5)(3x + 2):

(2x - 5)(3x + 2) = 2x * 3x + 2x * 2 - 5 * 3x - 5 * 2
= 6x^2 + 4x - 15x - 10
= 6x^2 - 11x - 10

Next, we multiply the terms inside the second set of parentheses, (4x - 10)(5x + 4):

(4x - 10)(5x + 4) = 4x * 5x + 4x * 4 - 10 * 5x - 10 * 4
= 20x^2 + 16x - 50x - 40
= 20x^2 - 34x - 40

Finally, we subtract the second expression from the first:

(2x - 5)(3x + 2) - (4x - 10)(5x + 4) = (6x^2 - 11x - 10) - (20x^2 - 34x - 40)
= 6x^2 - 11x - 10 - 20x^2 + 34x + 40
= 6x^2 - 20x^2 - 11x + 34x - 10 + 40
= -14x^2 + 23x + 30

Therefore, the simplified expression is -14x^2 + 23x + 30.