Question

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Answer 1

EXPLANATION.

Question = 1.

⇒ 16a² + 4b² + 9c² - 16ab + 12bc - 24ac.

As we know that,

Formula of :

⇒ (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx.

Using this formula in the equation, we get.

⇒ (4a)² + (2b)² + (3c)² + 2(4a)(-2b) + 2(-2b)(-3c) + 2(-3c)(4a).

⇒ (4a - 2b - 3c)².

Question = 2.

⇒ 9a² + 16b² + 25c² + 24ab + 40bc + 30ac.

As we know that,

Formula of :

⇒ (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx.

Using this formula in the equation, we get.

⇒ (3a)² + (4b)² + (5c)² + 2(3a)(4b) + 2(4b)(5c) + 2(5c)(3a).

⇒ (3a + 4b + 5c)².

Question = 3.

⇒ 4x² + y² + z² - 4xy - 2yz + 4xz.

As we know that,

Formula of :

⇒ (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx.

Using this formula in the equation, we get.

⇒ (2x)² + (y)² + (z)² + 2(2x)(-y) + 2(-y)(z) + 2(2x)(z).

⇒ (2x - y + z)².