Question

evaluate (2x-3y+3z)^2

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Answer 1

Answer:

(2x-3y+3z)^2

=(2x)^2+(-3y)^2+(3z)^2+2.2x(-3y)+2.(-3y).3z+2.3z.2x

=4x^2+9y^2+9z^2-12xy-18yz+12xz

Answer 2

Answer :-

4x² + 9y² + 9z² - 12xy - 18yz + 12xz - 18xyz

Step-by-step explanation :-

The given expression is (2x - 3y + 3z)²

Identity used:

→ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac + abc

Solution:

In the given question,

• a = 2x
• b = -3y
• c = 3z

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac + abc

⇒ (2x - 3y + 3z)² = (2x)² + (-3y)² + (3z)² + 2(2x)(-3y) + 2(-3y)(3z) + 2(2x)(3z) + [(2x)(-3y)(3z)]

⇒ (2x - 3y + 3z)² = 4x² + 9y² + 9z² + (-12xy) + (-18yz) + 12xz + [-18xyz]

⇒ (2x - 3y + 3z)² = 4x² + 9y² + 9z² - 12xy - 18yz + 12xz - 18xyz

∴ [4x² + 9y² + 9z² - 12xy - 18yz + 12xz - 18xyz]