9(q+1)+6(q+1)^2
7(a-b)(a+b)-14(a+b)
4x^2(x+1)-6x(x+1)
do the same way as in the previous post. Just factor out repeated values, as in
7(a-b)(a+b) - 14(a+b)
7(a+b)(a-b-2)
9(q+1)+6(q+1)^2
=
9q +9 + 6q^2 + 16q + 6
=6q^2 + 25q + 15
7(a-b)(a+b)-14(a+b)
=
7(a^2 + ab -ab -b^2) -14a -14b
=7a^2 -7b^2 -14a -14b
4x^2(x+1)-6x(x+1)
=
4x^3 + 4x^2 -6x^2 -6x
=
4x^3 -2x^2 -6x
To simplify these expressions, we will use the distributive property to multiply and combine like terms.
1. Let's simplify the expression 9(q+1)+6(q+1)^2:
Step 1: Distribute the 9 and 6 to the terms inside the parentheses.
9(q+1) = 9q + 9
6(q+1)^2 = 6(q^2 + 2q + 1)
Step 2: Simplify the expression by combining like terms.
Now we have 9q + 9 + 6q^2 + 12q + 6.
Combine like terms: 6q^2 + (9q + 12q) + (9 + 6)
Simplify further: 6q^2 + 21q + 15
Therefore, 9(q+1) + 6(q+1)^2 simplifies to 6q^2 + 21q + 15.
2. Now let's simplify the expression 7(a-b)(a+b) - 14(a+b):
Step 1: Distribute the 7 and -14 to the terms inside the parentheses.
7(a-b) = 7a - 7b
-14(a+b) = -14a - 14b
Step 2: Simplify the expression by combining like terms.
Now we have 7a - 7b + (-14a - 14b).
Combine like terms: (7a - 14a) + (-7b - 14b)
Simplify further: -7a - 21b
Therefore, 7(a-b)(a+b) - 14(a+b) simplifies to -7a - 21b.
3. Finally, let's simplify the expression 4x^2(x+1) - 6x(x+1):
Step 1: Distribute the 4x^2 and -6x to the terms inside the parentheses.
4x^2(x+1) = 4x^3 + 4x^2
-6x(x+1) = -6x^2 - 6x
Step 2: Simplify the expression by combining like terms.
Now we have 4x^3 + 4x^2 + (-6x^2 - 6x).
Combine like terms: 4x^3 + (4x^2 - 6x^2) + (-6x)
Simplify further: 4x^3 - 2x^2 - 6x
Therefore, 4x^2(x+1) - 6x(x+1) simplifies to 4x^3 - 2x^2 - 6x.
These are the simplified forms of the given expressions.