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How to factorise I x power 6 - y power 6 2 x power 12- y power 12?
Explanation: The difference of squares identity can be written: a 2 − b 2 = ( a − b ) ( a b ) The difference of cubes identity can be written: a 3 − b 3 = ( a − b ) ( a 2 a b b 2 ) The sum of cubes identity can be written: a 3 b 3 = ( a b ) ( a 2 − a b b 2 ) So: x 6 − y 6 = ( x 3 ) 2 − ( y 3 ) 2 = ( x 3 − y 3 ) ( x 3 y 3 ) = ( x − y ) ( x 2 x y y 2 ) ( x y ) ( x 2 − x y y 2 ) If we allow Complex coefficients, then this reduces into linear factors: = ( x − y ) ( x − ω y ) ( x − ω 2 y ) ( x y ) ( x ω y ) ( x ω 2 y ) where ω = − 1 2 √ 3 2 i = cos ( 2 π 3 ) sin ( 2 π 3 ) i is the primitive Complex cube root of 1 .
How minus times minus is plus?
Let y= ab+(- a)(b) +(-a)(-b) factor out -a y= ab+(-a){b+(-b)} y=ab+(-a)(0) y =ab -------------------(1) now factor out b y= b{a+(-a)}+(-a)(-b) y= b(0) +(-a)(-b) y= (-a)(-b)-----------------(2) equate (1) and (2) (-a)(-b)=ab minus x minus = positive
What is the slope and y intercept y equals x plus 2?
y=x+2 This equation is in the form of y=mx+b. Where m=the slope and b=y intercept. In this particular equation m=1 so the slope is 1 b=2 so the y intercept will be 2
How do you write the equation of a line that passes through the point 4 and -2 and has a slope of 2?
The standard form eqaution for a line is y = mx + b where m = slope and b is y intercept ( value of y when x = 0) if x = 4 and y = -2 and m = 2 then y = mx + b (eq 1) -2 = 2 (4) + b -2 = 8 + b -10 = b substitute into eq (1): y = 2x-10
How do you do a graph an equation?
finding the equation of a line of (-1,2) and (1,2): formula: y=mx+b m = slope b = y intercept first find m: m=(y2-y1)/(x2-x1) so, m=(2-2)/ (1- -1) m=0 since you now know m you can plug that in to the formula: y=0x+b to get b: plug in the coordinates (either (-1,2) or (1,2)), it comes out the same (-1,2). y=mx+b or 2=0 × -1+b, ==>solving for b: b=2-(0)(-1). b=2 (1,2). y=mx+b or 2=0 × 1+b, ==>solving for b: b=2-(0)(1). b=2 you now know that m=0 and b=2, now plug that back in the equation to get: y=mx+b y=0x+2 y+2 It's confusing, but it works!
