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Answer:
1) (-4a + 2b + 3c)(-4a + 2b + 3c)
2) (3a + 4b + 5c)(3a + 4b + 5c)
3) (2x - y + z)(2x - y + z)
Explanation:
1) 16a² + 4b² + 9c² - 16ab + 12bc - 24ac
= (-4a)² + (2b)² + (3c)² - 2×4×2ab + 2×3×2bc - 2×4×3ac
= (-4a + 2b + 3c)²
= (-4a + 2b + 3c)(-4a + 2b + 3c)
[writing like this is important when factorising. You'll thank me later for this.]
2) 9a² + 16b² + 25c² + 24ab + 40bc + 30ac
= (3a)² + (4b)² + (5c)² + 2×3×4ab + 2×4×5bc + 2×3×5ac
= (3a + 4b + 5c)²
= (3a + 4b + 5c)(3a + 4b + 5c)
3) 4x² + y² + z² - 4xy - 2yz + 4xz
= (4x)² + (-y)² + (z)² - 2×2xy - 2yz + 2×2xz
= (2x - y + z)²
= (2x - y + z)(2x - y + z)
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