Question

(3p+2)(5p-1) Show your work please

Answer 1

What is the factored form of the following expressions?
x^2-10xy+24y^2
show work please

Answer 2

When we apply the distributive property, we get:

(3p + 2)(5p - 1) = 3p × 5p + 3p × (-1) + 2 × 5p + 2 × (-1)

Simplifying the expression, we get:

15p² - 3p + 10p - 2 = 15p² + 7p - 2

Therefore, (3p + 2)(5p - 1) simplifies to 15p² + 7p - 2.

Answer 3

To factor x^2-10xy+24y^2, we need to find two numbers whose product is 24y^2 and whose sum is -10xy. These numbers are -4y and -6y.

Using these numbers, we can rewrite the middle term as -4xy - 6xy, which allows us to factor by grouping:

x^2 - 10xy + 24y^2 = x^2 - 4xy - 6xy + 24y^2
= (x^2 - 4xy) - (6xy - 24y^2)
= x(x - 4y) - 6y(x - 4y)
= (x - 6y)(x - 4y)

Therefore, the factored form of x^2-10xy+24y^2 is (x - 6y)(x - 4y).