expand (2a-b-3c)square
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Answer- The above question is from the chapter 'Polynomials'.
Polynomial- It is an algebraic expression involving use of variables and constants.
p(x)- It is used to denote a polynomial. It is read is 'Polynomial in x'.
Important identities:
1) (a+b)² = a² + 2ab + b²
2) (a-b)² = a² - 2ab + b²
3) (a+b)(a-b) = a² - b²
4) (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ac
Concept used: (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ac
Given question: Expand (2a + b - 3c)².
Solution: (2a + b - 3c)²
= [2a + b + (-3c)]²
Now, using the identity of (A + B + C)² where A = 2a, B = b and C = -3c, we get,
= (2a)² + (b)² + (-3c)² + 2 × 2a × b + 2 × b × -3c + 2 × -3c × 2a
= 4a² + b² + 9c² + 4ab - 6bc - 12ac
∴ The value of (2a + b - 3c)² = 4a² + b² + 9c² + 4ab - 6bc - 12ac.
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