How do I factorize 4x^4 - 25x^2 + 36?
One of the simplest way that I know is:Let x^2 = aThen equation is 4(x^2)^2–25x^2+364a^2–25a+36 = 04a^2-a(16+9)+36 = 04a^2–16a-9a+36 = 04a(a-4)-9(a-4) = 0(a-4) (4a-9) = 0Here,(a-4) = 0 and (4a-9) = 0a = 4 and a = 9/4First let a = 4Then, x^2 = 4x = 2Now let a = 9/4Then, x^2 = 9/4x = 3/2(°_~)
Please help factor fully 16x^3-40x^2+25x also solve-4x^4+60^3=200x^2?
16x^3-40x^2+25x =x[16x^2 --40x +25] =x[(4x)^2-2x(4)x(5)+ (5)^2] =x[4x-5][4x-5] **************************************... solve- 4x^4+60^3=200x^2 4x^4-- 200x^2 +60^3=0 4x^4 -200x^2\ +216000=0 x^4 --50x^2 +54000=0 LET x^2= y then y^2--50 y+54000=0
How do I factorise 16x^5-144x^2?
x^2 is one of the factors, the second common numerical factor would be 16. Hence the equation will be simplified to16x^2(x^3 - 9)
How do you factor (3x+5) ²-(5x-1) ²?
[math]X^2 - Y^2 = (X - Y).(X + Y)[/math]So,[math](3x + 5)^2 - (5x - 1)^2 [/math][math]\implies (3x + 5 - 5x + 1).(3x + 5 + 5x - 1)[/math][math]\implies (6 - 2x).(8x + 4)[/math][math]\implies 8.(3 - x).(2x + 1)[/math]
How can I factorize [math](4x -1) (7x +3) - (x + 3) (-4x + 1)[/math]?
(4x - 1)(7x + 3) - (x + 3)(-4x + 1) = Take the - sign in the middle and distribute it over the last factor. Make the sign in the middle +. (4x - 1)(7x + 3) + (x + 3)(4x - 1) =Factor 4x - 1 out of both terms. (4x - 1)(7x + 3 + x + 3) =Simplify the 2nd factor. (4x - 1)(8x + 6) = Factor 2 out of 2nd factor. 2(4x - 1)(4x + 3) ANSWER
Factor 16x^2 + 40xy + 25y^2?
16x^2 + 40xy + 25y^2 =16x^2 + 20xy +20xy+ 25y^2 = 4x(4x+5y) +5y(4x+5y) =(4x+5y)(4x+5y) =(4x+5y)^2
How do I factorise the expression [math]256x^{16}-1^2[/math]?
(2^8)(x^16 )=1(16)²(x^8)²=1(16x^8)²—1²=0(16x^8+1)(16x^8–1)=0 ......FOR SOLVING EQUATION......NOT asked for......overdone, sorryFOR FACTORISATION :Given expression ≡(16x^8+1){(4x^4)²—1²}=(16x^8+1)( 4x^4+1)( 4x^4–1)★★↘(i) EITHER 16x^8=1x^8=1/16x^8={±(1/√2 )}^8x=±(1√2) or x=±(√2)/2...............①↙↘↘(ii) OR 16x^8=—1x^8=-1/16=i²/16=(i^1/4)^8/(√2)^8x=±(i¼/√2=i¼/4¼)......x=±(i/4)¼....................................②↙↙∴Solutions: x=±(√2)/2 OR x=±(i/4)¼★★→Factored form=(16x^8+1)(4x^4+1)(4x^4–1)