Factorise- 4y2- 4y - 1 - Maths Q-A

Factorise the polynomial4y^2 4y+10ex0ex=4y^2 2y 2y+10ex0ex=2y(2y 1) 1(2y 1)0ex0ex=(2y 1)(2y 1)0ex0ex=(2y 1)^2Hence, the factors of 4y^2 4y+1 is (2y 1)^2. ...

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Standard X

Mathematics

Division Algorithm for a Polynomial

Factorise: 4y...

Question

Factorise: $4 y^{2} - 4 y + 1$

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Solution

Factorise the polynomial
$4 y^{2} - 4 y + 1 = 4 y^{2} - 2 y - 2 y + 1 = 2 y (2 y - 1) - 1 (2 y - 1) = (2 y - 1) (2 y - 1) = {(2 y - 1)}^{2}$
Hence, the factors of $4 y^{2} - 4 y + 1$ is ${(2 y - 1)}^{2}$ .

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Factorise: 4y2-4y+1

Factorise the polynomial4y2-4y+1=4y2-2y-2y+1=2y(2y-1)-1(2y-1)=(2y-1)(2y-1)=(2y-1)2Hence, the factors of 4y2-4y+1 is (2y-1)2.

Factorise: $4 y^{2} - 4 y + 1$

Factorise the polynomial
$4 y^{2} - 4 y + 1 = 4 y^{2} - 2 y - 2 y + 1 = 2 y (2 y - 1) - 1 (2 y - 1) = (2 y - 1) (2 y - 1) = {(2 y - 1)}^{2}$
Hence, the factors of $4 y^{2} - 4 y + 1$ is ${(2 y - 1)}^{2}$ .