(x+1)(x+2)=
(x+5)(x+6)=
(x+2)(x+7)=
(2x+3)(3x+1)=
(x+6)(x+6)=
(2x+3)(2x+3)=
(x+3) to the second power=
(x-5)to the second power=
(3x+2) to the second power=
(5x-3)to the second power=
I will be happy to critique your work. We just don't do homework for you.
I don't have text book I asked a friend for the questions and they couldn't help me
To find the product of two binomials, we can use the FOIL method. FOIL stands for First, Outer, Inner, and Last. Let's go through each equation step by step:
1. (x+1)(x+2)
Using the FOIL method:
First: x * x = x^2
Outer: x * 2 = 2x
Inner: 1 * x = x
Last: 1 * 2 = 2
Combine all the terms: x^2 + 2x + x + 2
Simplify the expression: x^2 + 3x + 2
2. (x+5)(x+6)
Using the FOIL method:
First: x * x = x^2
Outer: x * 6 = 6x
Inner: 5 * x = 5x
Last: 5 * 6 = 30
Combine all the terms: x^2 + 6x + 5x + 30
Simplify the expression: x^2 + 11x + 30
3. (x+2)(x+7)
Using the FOIL method:
First: x * x = x^2
Outer: x * 7 = 7x
Inner: 2 * x = 2x
Last: 2 * 7 = 14
Combine all the terms: x^2 + 7x + 2x + 14
Simplify the expression: x^2 + 9x + 14
4. (2x+3)(3x+1)
Using the FOIL method:
First: 2x * 3x = 6x^2
Outer: 2x * 1 = 2x
Inner: 3 * 3x = 9x
Last: 3 * 1 = 3
Combine all the terms: 6x^2 + 2x + 9x + 3
Simplify the expression: 6x^2 + 11x + 3
5. (x+6)(x+6)
Using the FOIL method:
First: x * x = x^2
Outer: x * 6 = 6x
Inner: 6 * x = 6x
Last: 6 * 6 = 36
Combine all the terms: x^2 + 6x + 6x + 36
Simplify the expression: x^2 + 12x + 36
6. (2x+3)(2x+3)
Using the FOIL method:
First: 2x * 2x = 4x^2
Outer: 2x * 3 = 6x
Inner: 3 * 2x = 6x
Last: 3 * 3 = 9
Combine all the terms: 4x^2 + 6x + 6x + 9
Simplify the expression: 4x^2 + 12x + 9
7. (x+3)^2
This equation is an example of squaring a binomial. To simplify, we can use the formula (a + b)^2 = a^2 + 2ab + b^2.
In this case, a = x and b = 3.
Using the formula, we get:
x^2 + 2(x)(3) + 3^2
Simplifying the expression:
x^2 + 6x + 9
8. (x-5)^2
Similar to the previous equation, we use the formula (a - b)^2 = a^2 - 2ab + b^2.
In this case, a = x and b = 5.
Using the formula, we get:
x^2 - 2(x)(5) + 5^2
Simplifying the expression:
x^2 - 10x + 25
9. (3x+2)^2
Again, we use the formula (a + b)^2 = a^2 + 2ab + b^2.
In this case, a = 3x and b = 2.
Using the formula, we get:
(3x)^2 + 2(3x)(2) + 2^2
Simplifying the expression:
9x^2 + 12x + 4
10. (5x-3)^2
The formula (a - b)^2 = a^2 - 2ab + b^2 still applies.
In this case, a = 5x and b = 3.
Using the formula, we get:
(5x)^2 - 2(5x)(3) + 3^2
Simplifying the expression:
25x^2 - 30x + 9
Remember, to find the product of two binomials, use the FOIL method. And to find the square of a binomial, use the appropriate formula for squaring binomials.