Which of the following answers apply for the distribution distributive property of multiplication over addition correctly simplifying 23 - 9 ( 2x + 5) plus 11X
To simplify the given expression using the distributive property of multiplication over addition, we need to distribute the number or expression outside the parentheses to each term inside the parentheses.
23 - 9(2x + 5) + 11x
Applying the distributive property:
= 23 - 9(2x) - 9(5) + 11x
= 23 - 18x - 45 + 11x
Now, let's combine like terms:
= (23 - 45) + (-18x + 11x)
= -22 - 7x
Therefore, the simplified form of the expression is -22 - 7x.
Simplify -4 ( 7b + 3 ) + 24b - 8
To simplify the given expression using the distributive property of multiplication over addition:
-4(7b + 3) + 24b - 8
Apply the distributive property:
= -4 * 7b + (-4 * 3) + 24b - 8
= -28b - 12 + 24b - 8
Now combine like terms:
= (-28b + 24b) + (-12 - 8)
= -4b - 20
Therefore, the simplified form of the expression is -4b - 20.
Simplify 2 (3v+9) - 14 - 6 (-5v - 4)
To simplify the given expression using the distributive property of multiplication over addition:
2(3v + 9) - 14 - 6(-5v - 4)
Let's apply the distributive property:
= 2 * 3v + 2 * 9 - 14 - 6 * (-5v) - 6 * (-4)
= 6v + 18 - 14 + 30v + 24
Now combine like terms:
= (6v + 30v) + (18 + 24 - 14)
= 36v + 28
Therefore, the simplified form of the expression is 36v + 28.
-15+ 4/5(15e - 10) - 10e
To simplify the given expression using the distributive property of multiplication over addition:
-15 + (4/5)(15e - 10) - 10e
Let's apply the distributive property:
= -15 + (4/5)(15e) + (4/5)(-10) - 10e
= -15 + (4/5)(15e) - (4/5)(10) - 10e
Simplify the multiplication:
= -15 + (4/5)*15e - (4/5)*10 - 10e
= -15 + (60/5)e - (40/5) - 10e
= -15 + 12e - 8 - 10e
Combine like terms:
= (-15 - 8) + (12e - 10e)
= -23 + 2e
Therefore, the simplified form of the expression is -23 + 2e.
Factor 48y + 36z using the GCF
To factor 48y + 36z using the greatest common factor (GCF), we need to find the largest factor that can be divided evenly into both terms.
The prime factorization of 48 is:
48 = 2 * 2 * 2 * 2 * 3
The prime factorization of 36 is:
36 = 2 * 2 * 3 * 3
The GCF of 48 and 36 can be found by taking the product of the common prime factors raised to the lowest exponent. In this case, that would be 2 * 2 * 3 = 12.
Now we can rewrite the expression 48y + 36z as follows:
48y + 36z = 12 * (4y + 3z)
Therefore, the factored form of 48y + 36z using the GCF is 12(4y + 3z).