Square of trinomial
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The document provides a formula and examples for finding the square of a trinomial. The formula is: F2 + M2 + L2 + 2FM + 2FL + 2ML, where F is the first term, M is the middle term, L is the last term, and the other terms represent twice the product of the terms. It then works through four examples applying the formula to find the square of trinomials such as (a + b + c)2, (x + y - 3)2, (x - 2y - 1)2, and (2a - b + b2)2.
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Square of trinomial
- 2. To solve square of trinomial use the formula of F2 + M2 + L2 + 2FM + 2FL + 2ML Where, F2 = square the first term M2 = square middle term L2 = square the last term 2FM = twice the product of the first and second term 2FL = twice the product of the first and last term 2ML = twice the product of the middle term and the last term
- 3. Example 1. Find the product of (a + b + c)2 . Solution: Using the formula of F2 + M2 + L2 + 2FM + 2FL + 2ML F2 = (a)2 = a2 M2 = (b)2 = b2 L2 = (c)2 = c2 2FM = 2(a . b) = 2ab 2FL = 2(a. c) = 2ac 2ML = 2(b . c) = 2bc = a2 + b2 + c2 + 2ab + 2ac + 2bc
- 4. Example 2. Find the product of (x + y – 3)2 . Solution: Using the formula of F2 + M2 + L2 + 2FM + 2FL + 2ML F2 = (x)2 = x2 M2 = (y)2 = y2 L2 = (-3)2 = 9 2FM = 2(x. y) = 2xy 2FL = 2(x . -3) = -6x 2ML = 2(y . -3) = -6y = x2 + y2 + 9 + 2xy – 6x – 6y = x2 + 2xy + y2 – 6x – 6y + 9
- 5. Example 3. Find the product of (x – 2y – 1)2. Solution: Using the formula of F2 + M2 + L2 + 2FM + 2FL + 2ML F2 = (x)2 = x2 M2 = (-2y)2 = 4y2 L2 = (-1)2 = 1 2FM = 2(x. -2y) = -4xy 2FL = 2(x -1) = -2x 2ML = 2(-2y . -1) = 4y = x2 + 4y2 + 1 – 4xy – 2x + 4y = x2 -4xy + 4y2 – 2x + 4y + 1
- 6. Example 4. Solve (2a – b + b2)2. Solution: Using the formula of F2 + M2 + L2 + 2FM + 2FL + 2ML F2 = (2a)2 = 4a2 M2 = (-b)2 = b2 L2 = (b2)2 = b4 2FM = 2(2a . –b) = -4ab 2FL = 2(2a . b2) = 4ab2 2ML = 2(-b . b2) = -2b3 = 4a2 + b2 + b4 – 4ab + 4ab2 – 2b3 = 4ab2 +4a2– 4ab + b4 - 2b3 + b2