special factor patterns
TRANSCRIPT
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1. Write as a Binomial:
(9-w)(9+w)
2. Write each square as a trinomial:
(6c-1)²
3. Simplify:
(y+4)(y+10)
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a²-b² (a+b)(a-b)
(First #)² - (Second #)² = (sum of 2 squares) x (their
difference)
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Ex:9a²-4b²=(3a+2b)(3a-2b)
3a is the square root of 9a² and 2b is the square root of 4b²
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Ex:36-25
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81-16
***After you factor the number the first time, if there still is an a²-b² in the subtraction binomial, you have to factor again until there are no squares left.***
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a²+(-)2ab+b² (a+(-)b)²
If the middle number in the equation equals twice the square root of a
times the square root of b, then you can factor it.
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Ex: a²+2a+1= (a+1)²
a and 1 are the square roots of the first and last numbers
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Ex:u²-6u+9
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Ex:b²+12b+4
This trinomial can’t be factored this way because the middle number does not equal twice the product of the first and last number.
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Ex:121c^4-264c²+144
^4 means to the fourth power****
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x²+(-)bx+c (x + factor of b that adds to c) (x +(-) factor of b
that adds to c)
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Ex: x²+8x+15 = (x+3) (x+5)
5 and 3 add up to 8, and are a factor pair of 15.
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Ex:x²-10x+24
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Ex:y²+20yz+91z²
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Ex:x^4-15x²y²-16y^4
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