5. Factorise:
(i) 4x2 +9y2 + 16z2 + 12xy – 24yz - 16xz
(ii) 2x2 + y2 + 8z2 – 22 xy + 412 yz – 8
Answers
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)
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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:
Ⓗⓔⓡⓔ'ⓢ ⓨⓞⓤⓡ ⓐⓝⓢⓦⓔⓡ ⓜⓐⓣⓔ!
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•◍)❤