Square of a Trinomial By: Mr.Jay Mar Bolajo

( x + y + z) = x2 + y2 + z2 + 2xy + 2xz + 2yz Square the first term Square the second term Square the third term Twice the product of 1st and 2nd terms Twice the product of 1st and 3rd terms Twice the product of 2nd and 3rd terms

Examples (2a+2b+2c)2 = (2a)2 + (2b)2 + (2c)2 + 2(2a)(2b) + 2(2a)(2c) + 2(2b)(2c) = 4a2 + 4b2 + 4c2 + 8ab + 8ac + 8bc

Examples (x + 2y – 3)2 = x2 + (2y)2 + (-3)2 + 2(x)(2y) + 2(x)(-3) + 2(2y)(-3) = x2 + 4y2 + 9 + 4xy – 6x – 12y

Try this! (3m – n + 1)2

Answer 9m2 + n2 + 1 – 6mn + 6m – 2n

Try this! Expand: ( x + 3y + 4z)2

Answer x2 + 9y2 + 16z2 + 6xy + 6xz + 24 yz

Try this! Find the expansion of ( 4r – 5s – 2t)2

Answer 16r2 + 25s2 + 4t2 - 40rs – 16rt + 20st

Skill Practice: Find the product of the following. ( a – b + c )2 (2x + 3y + 4)2 (3x – 2y + 4)2 (5x + 3y – 2)2 (x – 2y + 5)2

Answers a2 + b2 + c2 -2ab + 2ac -2bc 4x2 + 9y2 + 16 + 12xy + 16x + 24y

Homework (a + 2b – c)2 (5x – 2y + 1)2 (8x – 2y + 3)2 (3x2 – 2y2 + 1)2 Find the expanded form of the following. (a + 2b – c)2 (5x – 2y + 1)2 (8x – 2y + 3)2 (3x2 – 2y2 + 1)2 ( x3 + y2 + 4)2