Advertisements
Advertisements
Question
Factorize each of the following expression:
(2x + 1)2 − 9x4
Advertisements
Solution
\[(2x + 1 )^2 - 9 x^4 \]
\[ = (2x + 1 )^2 - (3 x^2 )^2 \]
\[ = [(2x + 1) - 3 x^2 ][(2x + 1) + 3 x^2 ]\]
\[ = ( - 3 x^2 + 2x + 1)(3 x^2 + 2x + 1)\]
We can factorise the quadratic expressions in the curved brackets as:
\[( - 3 x^2 + 3x - x + 1)(3 x^2 + 2x + 1)\]
\[ = \left\{ 3x( - x + 1) + 1( - x + 1) \right\}(3 x^2 + 2x + 1)\]
\[ = ( - x + 1)(3x + 1)(3 x^2 + 2x + 1)\]
\[ = - (x - 1)(3x + 1)(3 x^2 + 2x + 1)\]
RELATED QUESTIONS
Factorize each of the following expression:
125x2 − 45y2
Factorize each of the following expression:
(2a − b)2 − 16c2
Factorize each of the following expression:
(x + 2y)2 − 4(2x − y)2
Factorize each of the following expression:
25x4y4 − 1
Factorize each of the following expression:
(3 + 2a)2 − 25a2
Factorize each of the following expression:
(x + y)2 − (a − b)2
Factorize each of the following quadratic polynomials by using the method of completing the square:
x2 + 12x + 20
Factorize each of the following quadratic polynomials by using the method of completing the square:
a2 − 14a − 51
Factorize each of the following quadratic polynomials by using the method of completing the square:
a2 + 2a − 3
Factorize each of the following quadratic polynomials by using the method of completing the square:
y2 − 7y + 12
