1- (2x-4)(x+5)
Multiplying using the distributive property, we get:
(2x-4)(x+5) = 2x(x) + 2x(5) - 4(x) - 4(5)
= 2x^2 + 10x - 4x - 20
= 2x^2 + 6x - 20
Therefore, (2x-4)(x+5) simplifies to 2x^2 + 6x - 20.
2-(x-2)^2
Expanding using the formula for the square of a binomial, we get:
(x-2)^2 = x^2 - 4x + 4
Therefore, (x-2)^2 simplifies to x^2 - 4x + 4.
3- (3x+1)^2
Expanding using the formula for the square of a binomial, we get:
(3x+1)^2 = (3x)^2 + 2(3x)(1) + (1)^2
= 9x^2 + 6x + 1
Therefore, (3x+1)^2 simplifies to 9x^2 + 6x + 1.
4- (3x-1)(2x^2+5x-4)
Using the distributive property, we can multiply each term in the first polynomial by each term in the second polynomial:
(3x-1)(2x^2+5x-4) = 3x(2x^2) + 3x(5x) - 3x(4) - 1(2x^2) - 1(5x) + 1(4)
= 6x^3 + 15x^2 - 12x - 2x^2 - 5x + 4
= 6x^3 + 13x^2 - 17x + 4
Therefore, (3x-1)(2x^2+5x-4) simplifies to 6x^3 + 13x^2 - 17x + 4.