I need some help multiplying these two sets of binomials.
1. (x+5)(x+3) so I think the answer to this one is x^2+15 is this correct?
2. (x-5)(x+3) I think the answer to this one is x^2-15 but how do you know when to make it a + or a - in the solution?
1. WHat is 5 times x, Plus x times 3?
2. What is -5*x plus + 3*x ?
To find the product of two binomials, you can use the distributive property of multiplication. Let's break it down:
1. (x+5)(x+3)
To multiply these two binomials, you can use the FOIL method, which stands for First, Outer, Inner, Last. First, multiply the first terms of each binomial, then the outer terms, inner terms, and finally the last terms.
First term: x * x = x^2
Outer term: x * 3 = 3x
Inner term: 5 * x = 5x
Last term: 5 * 3 = 15
Now, add up all the terms:
x^2 + 3x + 5x + 15
Combine like terms:
x^2 + 8x + 15
So, the answer is x^2 + 8x + 15. You were close, but the middle term should be 8x, not just 15.
2. (x-5)(x+3)
Similar to the previous example, we will use the FOIL method.
First term: x * x = x^2
Outer term: x * 3 = 3x
Inner term: -5 * x = -5x
Last term: -5 * 3 = -15
Now, add up all the terms:
x^2 + 3x - 5x - 15
Combine like terms:
x^2 - 2x - 15
As you mentioned, you correctly subtracted -15. The signs in the middle terms are determined by the signs in the original binomials. In this case, the second binomial is (x+3), so when multiplying x with -5, you get -5x. Hence, the middle term is -2x.
So, the answer is x^2 - 2x - 15. Great job!