The only thing left is:(x+2)(x+2)Which is (x+2)^2-You have to come up with a way to multiple and get 4x and add and get the 4 on the right. 2 x 2= 4 2+ 2= 4 (x^2 + 2x) + (2x + 4) x(x+ 2) + 2( x+ 2)(defoiling) (x+2) (x+2)This is the way that I learned how to do it.-x^2 + 4x + 4sqrt(x^2) = xsqrt(4) = 22*x*2 = 4*xTherefore,x^2 + 4x + 4 = (x + 2)^2x^2 - 2x + 1sqrt(x^2) = xsqrt(1) = 1 - 2*x*1 = - 2*xTherefore,x^2 - 2x + 1 = (x - 1)^2-1).x^2 + 4x + 4= x^2 + 2x + 2x + 4= x(x + 2) + 2(x + 2)=(x + 2)(x + 2)=(x + 2)^22).......
x² + 4x + 4 --------------> replace 4x with 2x + 2x
= x² + 2x + 2x + 4 -----> factor in pairs
= (x² + 2x) + (2x + 4)
= x (x + 2) + 2 (x + 2) -----> now factor out (x + 2)
= (x + 2) (x + 2)
= (x + 2)²
______________________________
x² − 2x + 1
To factor in form (x + a) (x + b) you need to find two numbers (a and b)
whose product = constant factor = 1 and
whose sum = coefficient of x = −2
(−1) * (−1) = 1
(−1) + (−1) = −2
So a = −1, b = −1
x² − 2x + 1 = (x − 1) (x − 1) = (x − 1)²
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Alternatively, you can factor in pairs:
x² − 2x + 1 --------------> replace −2x with −x − x
= x² − x − x + 1 --------> factor in pairs
= (x² − x) + (− x + 1)
= x (x − 1) − 1 (x − 1) -----> now factor out (x − 1)
= (x − 1) (x − 1)
= (x − 1)²
Mαthmφm
You have to come up with a way to multiple and get 4x and add and get the 4 on the right.
2 x 2= 4
2+ 2= 4
(x^2 + 2x) + (2x + 4)
x(x+ 2) + 2( x+ 2) (defoiling)
(x+2) (x+2)
This is the way that I learned how to do it.
1).
x^2 + 4x + 4
= x^2 + 2x + 2x + 4
= x(x + 2) + 2(x + 2)
= (x + 2)(x + 2)
= (x + 2)^2
2).
x^2 - 2x + 1
= x^2 + x + x + 1
= x(x + 1) + (x + 1)
= (x + 1)(x + 1)
= (x + 1)^2
