Factorize (i) 9x 2 – y 2 (ii) (3 – x) 2 – 36x 2 (iii) (2x – 3y) 2 – (3y + 4y) 2 (iv) 16x 4 – y 4

Question

Factorize (i) 9x 2 &#x2013; y 2 (ii) (3 &#x2013; x) 2 &#x2013; 36x 2 (iii) (2x &#x2013; 3y) 2 &#x2013; (3y + 4y) 2 (iv) 16x 4 &#x2013; y 4

Philoid · Accepted Answer

(i) 9x² – y² = (3x)² – (y)²
= (3x + y)(3x – y)

(ii) (3 – x)² – 36x²= (3 – x)² – (6x)²= (3 - x + 6x) (3 - x - 6x)
= (3 + 5x)(3 – 7x)

(iii) (2x – 3y)² – (3x + 4y)²= (2x – 3y + 3x + 4y)(2x – 3y – 3x – 4y)
= (5x + y)(- x – 7y)
= -(5x + y) (x + 7y)

(iv) 16x⁴ – y⁴ = (4x²)² – (y²)²= (4x² + y²)(4x² –y²)
= (4x² + y²)(2x + y) (2x - y)

Factorize(i) 9x2 – y2(ii) (3 – x)2 – 36x2(iii) (2x – 3y)2 – (3y + 4y)2(iv) 16x4 – y4

Factorize
(i) 9x² – y²
(ii) (3 – x)² – 36x²
(iii) (2x – 3y)² – (3y + 4y)²
(iv) 16x⁴ – y⁴