6x(2x+3)
To simplify the expression 6x(2x+3), you will need to distribute the 6x to both terms inside the parentheses (2x and 3).
6x times 2x = 12x^2
6x times 3 = 18x
So the simplified expression is 12x^2 + 18x.
(8p-2)(6p+2)
To simplify the expression (8p-2)(6p+2), you will need to distribute both terms 8p and -2 to both terms inside the second parentheses (6p and 2).
(8p)(6p) = 48p^2
(8p)(2) = 16p
(-2)(6p) = -12p
(-2)(2) = -4
Now, combine like terms:
48p^2 + 16p - 12p - 4
Combine 16p and -12p:
48p^2 + 4p - 4
So the simplified expression is 48p^2 + 4p - 4.
(4y-1)^2
To simplify the expression (4y-1)^2, you will need to expand the square by multiplying the expression by itself.
(4y-1)^2 = (4y-1)(4y-1)
Using the FOIL method (First, Outer, Inner, Last), multiply each term:
First: (4y)(4y) = 16y^2
Outer: (4y)(-1) = -4y
Inner: (-1)(4y) = -4y
Last: (-1)(-1) = 1
Combine like terms:
16y^2 - 4y - 4y + 1
Simplify:
16y^2 - 8y + 1
So the simplified expression is 16y^2 - 8y + 1.
(4a+2)(6a^2-a+2)
To simplify the expression (4a+2)(6a^2-a+2), you need to distribute each term of the first expression to each term in the second expression.
First, distribute 4a to each term in the second expression:
4a * 6a^2 = 24a^3
4a * (-a) = -4a^2
4a * 2 = 8a
Now, distribute 2 to each term in the second expression:
2 * 6a^2 = 12a^2
2 * (-a) = -2a
2 * 2 = 4
Combining like terms, we have:
24a^3 - 4a^2 + 8a + 12a^2 - 2a + 4
Grouping like terms:
(24a^3) + (-4a^2 + 12a^2) + (8a - 2a) + 4
Simplifying:
24a^3 + 8a^2 + 6a + 4
So, the simplified expression is 24a^3 + 8a^2 + 6a + 4.
(6x^2-6x-5)(7x^2+6x-5)
To simplify the expression (6x^2-6x-5)(7x^2+6x-5), you need to distribute each term of the first expression to each term in the second expression.
First, distribute 6x^2 to each term in the second expression:
6x^2 * 7x^2 = 42x^4
6x^2 * 6x = 36x^3
6x^2 * -5 = -30x^2
Now, distribute -6x to each term in the second expression:
-6x * 7x^2 = -42x^3
-6x * 6x = -36x^2
-6x * -5 = 30x
Lastly, distribute -5 to each term in the second expression:
-5 * 7x^2 = -35x^2
-5 * 6x = -30x
-5 * -5 = 25
Combining like terms, we have:
42x^4 + 36x^3 - 30x^2 - 42x^3 - 36x^2 + 30x - 35x^2 - 30x + 25
Grouping like terms:
42x^4 + (36x^3 - 42x^3) + (-30x^2 - 36x^2 - 35x^2) + (30x - 30x) + 25
Simplifying:
42x^4 - 6x^3 - 101x^2 + 25
So, the simplified expression is 42x^4 - 6x^3 - 101x^2 + 25.
To simplify the expression 6x(2x+3), you can distribute the 6x to both terms inside the parentheses. Here's how:
1. Multiply 6x with 2x: 6x * 2x = 12x^2.
2. Multiply 6x with 3: 6x * 3 = 18x.
Therefore, the simplified expression is 12x^2 + 18x.