(3p+2)(5p-1) Show your work please
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.
What is the factored form of the following expressions?
x^2-10xy+24y^2
show work please
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).
To expand the expression (3p+2)(5p-1), you can use the distributive property.
First, distribute 3p to both terms of the second parenthesis:
(3p)(5p) + (3p)(-1)
Next, distribute 2 to both terms of the second parenthesis:
(2)(5p) + (2)(-1)
Simplify each term:
15p^2 - 3p + 10p - 2
Combine like terms:
15p^2 + 7p - 2
So, the expanded form of (3p+2)(5p-1) is 15p^2 + 7p - 2.