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:
\[( - 3 x^2 + 3x - x + 1)(3 x^2 + 2x + 1)\]
\[ = \left\{ 3x( - x + 1) + 1( - x + 1) \right\}(3 x^2 + 2x + 1)\]
\[ = ( - x + 1)(3x + 1)(3 x^2 + 2x + 1)\]
\[ = - (x - 1)(3x + 1)(3 x^2 + 2x + 1)\]
APPEARS IN
RELATED QUESTIONS
Factorize each of the following expression:
125x2 − 45y2
Factorize each of the following expression:
(x + y)2 − (a − b)2
Factorize each of the following expression:
256x5 − 81x
Factorize each of the following expression:
a4 − (2b + c)4
Factorize each of the following expression:
16(2x − 1)2 − 25y2
Factorize each of the following expression:
x3 − x
Factorize each of the following quadratic polynomials by using the method of completing the square:
p2 + 6p − 16
Factorise the following expressions
4x2 – 8x + 3
Factorise: (7y2 – 19y – 6)
A mason uses the expression x2 + 6x + 8 to represent the area of the floor of a room. If the decides that the length of the room will be represented by (x + 4), what will the width of the room be in terms of x?
