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:
36l2 − (m + n)2
Factorize each of the following expression:
(3 + 2a)2 − 25a2
Factorize each of the following expression:
\[\frac{1}{16} x^2 y^2 - \frac{4}{49} y^2 z^2\]
Factorize each of the following expression:
Factorize each of the following expression:
3x3y − 243xy3
Factorize each of the following quadratic polynomials by using the method of completing the square:
4x2 − 12x + 5
Factorize each of the following quadratic polynomials by using the method of completing the square:
y2 − 7y + 12
Factorize each of the following quadratic polynomials by using the method of completing the square:
z2 − 4z − 12
Obtain the factors of z2 – 4z – 12.
Factorise the following expressions
4x2 – 8x + 3
