Question

5. Factorise:
(i) 4x2 +9y2 + 16z2 + 12xy – 24yz - 16xz
(ii) 2x2 + y2 + 8z2 – 22 xy + 412 yz – 8​

Answer 1

1. 4x² + 9y² + 16z² + 12xy - 24yz - 16xz

↦ (2x)² + (3y)² + (-4z)² + 2(2x)(3y) + 2(3y) (-4z) (2x)

↦ (2x+3y−4z) 2

↦ (2x+3y−4z)(2x+3y−4z)

_________________

2. 2x² + y² + 8z² - 2 √2xy + 4√ 2yz - 8zx

↦ (-√2x) + (y)² + (√2z) + 2( - √2x) (y) + 2(y) (2√2z) + 2(2√2z)(y)

↦ (-√2x + y + 2√ 2z²)

↦ (-√2x + y + 2√2z ) (- √2x + y + 2√2z)

________________________

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Answer 2

Answer:

Ⓗⓔⓡⓔ'ⓢ ⓨⓞⓤⓡ ⓐⓝⓢⓦⓔⓡ ⓜⓐⓣⓔ!

4x2+ 9y2 + 16zஏ + 12xy - 24yz - 16xz

+ 16zஏ + 12xy - 24yz - 16xz↦ (2x)2 + (3y)2 + (-4z)2 + 2(2x)(3y) + 2(3y) (-4z) (2x)

+ 2(2x)(3y) + 2(3y) (-4z) (2x)↦ (2x+3y−4z) 2

+ 2(2x)(3y) + 2(3y) (-4z) (2x)↦ (2x+3y−4z) 2↦ (2x+3y−4z)(2x+3y−4z)

+ 2(2x)(3y) + 2(3y) (-4z) (2x)↦ (2x+3y−4z) 2↦ (2x+3y−4z)(2x+3y−4z)2. 2x2+ y2+ 8z2- 2 √2xy + 4√ 2yz - 8zx

- 2 √2xy + 4√ 2yz - 8zx↦ (-√2x) + (y)2 + (√2z) + 2( - √2x) (y) + 2(y) (2√2z) + 2(2√2z)(y)

+ (√2z) + 2( - √2x) (y) + 2(y) (2√2z) + 2(2√2z)(y)↦ (-√2x + y + 2√ 2z2)

)↦ (-√2x + y + 2√2z ) (- √2x + y + 2√2z)

Hope this helps you army!

Have bangastic dreams tonight (◍•ᴗ•◍)❤