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a^(2)- 2ab - 15b^(2)
When the first term has a coefficient of '1' (a^(2)), then look at the third term.
It is '15'. So we need two numbers that multiply to '15' and 'add/subtract'to '2'.
They are 3. & 5.
So writing up our brackets
( a 5b)(a 3b)
Which signs???
We note from the quadraic , that '15' is negative(-) . So the brackets need one positive(+) and one negative(-)
Since the middle term is also negative(-) , then the larger numerical number takes the negative.
Hence
( a - 5b)(a + 3b)
Done!!!!
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What is a3-4a when it is factored completely?
a3-4a = a(a2-4) when factored
How do you factor fully 'a4 plus 4b4?
(a2+2b2-2ab)(a2+2b2+2ab)
If the perfect square terms are A2 and B2 then the other term must be?
2AB
What is formula for a minus b whole square?
(a-b)2 = a2 _ 2ab+b2
Is a squared plus b squared the same as a plus b squared?
No. If you expand (a + b)2 you get a2 + 2ab + b2. This is not equal to a2 + b2
What is a3-4a when it is factored completely?
a3-4a = a(a2-4) when factored
How do you factor fully 'a4 plus 4b4?
(a2+2b2-2ab)(a2+2b2+2ab)
When do you say that a trinomial is a perfect square?
A trinomial is perfect square if it can be factored into the form (a+b)2 So a2 +2ab+b2 would work.
Are there numbers with the property that the sum of their squares equals the square of their sum?
Yes, as long as either number is 0. a2 + b2 = (a+b)2 a2 + b2 = a2 + 2ab + b2 0 = 2ab
How is the expansion of algebraic expressions done?
There are 3 main rules for expansion of algebraic expressions. They are as follows: 1) a2 _ b2 = (a-b) (a+b) 2) (a+b)2 = a2 + 2ab +b2 3) (a-b)2 = a2 - 2ab +b2
What is the simplified expression for 2a2b a2 5ab 3ab2 b2 2a2b 2ab?
I'm going to assume a few things... 1.) the 2s after a letter are 2 2.) this is addition, because it's easier for me and if you wanted another operation, you should have stated so. 2a2b+a2+5ab+3ab2+b2+2a2b+2ab 4ab+a2+5ab+3b2a+b2+4ab+2ab 15ab+3b2a+a2+b2
How do you cube a binomial?
let binomial be (a + b)now (a+b)3 will be (a+b)(a+b)2 = (a+b)(a2 + 2ab+ b2) = a(a2+ 2ab+ b2) + b(a2 + 2ab+ b2) = a3+ 2a2b+ ab2 + a2b + 2ab2 + b3 = a3+ 2a2b+ ab2 + a2b + 2ab2 + b3 = a3 +3a2b + 3ab2 +b3 hope it helped... :D
If the perfect square terms are A2 and B2 then the other term must be?
2AB
What is a perfect trianomial?
perfect trinomial square?? it has the form: a2 + 2ab + b2
What is Special Case Product of Binomial?
Some special cases that are relevant in practice are: (a + b)2 = a2 + 2ab + b2 (a - b)2 = a2 - 2ab + b2 (x + a)(x + b) = x2 + (a+b)x + ab
What is formula for a minus b whole square?
(a-b)2 = a2 _ 2ab+b2
What is the factor expression for a2-5a-14?
a2-5a-14 = (a-7)(a+2) when factored
