Factorize each of the following expression-2 x-12-9 x4

(2x+1)2 9x4=(2x+1)2 (3x2)2=[(2x+1) 3x2][(2x+1)+3x2]=( 3x2+2x+1)(3x2+2x+1)We #160;can #160;factorise #160;the #160;quadratic #160;expressions #160;in ...

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Standard VIII

Mathematics

Factors of Algebraic Expressions and Factorisation

Factorize eac...

Question

Factorize each of the following expression:
(2x + 1)² − 9x⁴

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Solution

$(2 x + 1)^{2} - 9 x^{4} = (2 x + 1)^{2} - (3 x^{2})^{2} = [(2 x + 1) - 3 x^{2}] [(2 x + 1) + 3 x^{2}] = (- 3 x^{2} + 2 x + 1) (3 x^{2} + 2 x + 1) We can factorise the quadratic expressions in the curved brackets as : (- 3 x^{2} + 3 x - x + 1) (3 x^{2} + 2 x + 1) = \{3 x (- x + 1) + 1 (- x + 1)\} (3 x^{2} + 2 x + 1) = (- x + 1) (3 x + 1) (3 x^{2} + 2 x + 1) = - (x - 1) (3 x + 1) (3 x^{2} + 2 x + 1)$

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Factorize each of the following expression: (2x + 1)2 − 9x4

(2x+1)2-9x4=(2x+1)2-(3x2)2=[(2x+1)-3x2][(2x+1)+3x2]=(-3x2+2x+1)(3x2+2x+1)We can factorise the quadratic expressions in the curved brackets as:(-3x2+3x-x+1)(3x2+2x+1)=3x(-x+1)+1(-x+1)(3x2+2x+1)=(-x+1)(3x+1)(3x2+2x+1)=-(x-1)(3x+1)(3x2+2x+1)

Factorize each of the following expression:
(2x + 1)² − 9x⁴