1.) (t + 3 )(t + 2) First Term: t x t= x2 Outer: t x 2= 2t Inner: t x 3= 3t Last Term: 3 x 2= 6 Add Inner and Outer to get the middle term: 3t + 2t= 5t Answer: t2 + 5t + 6
2.) (k + 7 )( k - 4) First Term: k x k = k2 Outer: k x -4 = -4k Inner: 7 x k = 7k Last Term: 7 x -4 = -28 Add Inner and Outer to get the middle term: -4t + 7t= 3t Answer: k2 + 3k - 28
3.) (x + 3)(x2 + 2x + 4) x3 + 2x2 + 4x + 3x2 + 6x + 12 Group like terms: x3 + 2x2 + 3x2 + 4x + 6x + 12 Combine like terms: x3 + 5x2 + 10x + 12
4.) (x + 3)3 (x + 3)(x + 3)(x + 3) The first multiplication is done: (x2 + 3x + 3x + 9)(x + 3) Combine like terms and switch order: (x + 3) (x2 + 6x + 9) Multiply again: x3 + 6x2 + 9x + 3x2 + 18x + 27 Combine like terms: x3 + 9x2 + 27x + 27
5.) (2x2 + 2x + 1)(3x2 + 5x + 2) Step 1: 1. Multiply the first term of the first trinomial with each term of second trinomial: 2x2 x (3x2 + 5x + 2) = 6x4 + 10x3 + 4x2 2. Next, multiply the second term of the first trinomial with each term of the second trinomial: 2x x (3x2 + 5x + 2) = 6x3 + 10x2 + 4x 3. Finally, multiply the third term of the first trinomial with each term of the second trinomial: 1 x (3x2 + 5x + 2) = 3x2 + 5x + 2 Step 2: 1. Add 1, 2, and 3: 6x4 + 10x3 + 4x2 + 6x3 + 10x2 + 4x + 3x2 + 5x + 2 2. Group the like terms together: 6x4 + 10x3 + 6x3 + 4x2 + 10x2 + 3x2 + 4x + 5x + 2 3. Now, add the like terms and simplify: 6x4 + 16x3 + 17x2 + 9x + 2 4. Answer: 6x4 + 16 x3 + 17x2 + 9x + 2
Why would you want to be someone else When you could be better by being yourself Why pretend to be someone you are not When you have something they haven't got Cheating yourself of the life you have to live Deprives others of that only which you can give You have much more to offer by being just you Than walking around in someone else's shoes Trying to live the life of another is a mistake It is a masquerade; nothing more than a fake Be yourself and let your qualities show through Others will love you more for being just you Remember that God loves you just as you are To Him you are already a bright shining star Family and friends will love you more too If you spent time practicing just being you
The children who's parents are waiting outside are triplets.
The children who's whose parents are waiting outside are triplets.
Between the five suspects, who do you think did it?
Between Among the five suspects, who do you think did it?
How I wish my sister was here!
How I wish my sister was were here!
Either a cow or carabao plow the fields.
Either a cow or carabao plow plows the fields.
Romeo and Juliet are one of Shakespeare's greatest literary works.
Romeo and Juliet are is one of Shakespeare's greatest literary works.