SQUARE OF A TRINOMIAL WORKSHEET
Problem 1 :
Expand :
(5x + 3y + 2z)2
Problem 2 :
If a + b + c = 15 , ab + bc + ac = 25, then find the value of
a2 + b2 + c2
Problem 3 :
Expand :
(x + 2y - z)2
Problem 4 :
Expand :
(3x - y + 2z)2
Problem 5 :
Expand :
(x - 2y - 3z)2
Answers
Problem 1 :
Expand :
(5x + 3y + 2z)2
Solution :
(5x + 3y + 2z)2 is in the form of (a + b + c)2
Comparing (a + b + c)2 and (5x + 3y + 2z)2, we get
a = 5x
b = 3y
c = 2z
Write the formula / expansion for (a + b + c)2.
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
Substitute 5x for a, 3y for b and 2z for c.
(5x + 3y + 2z)2 :
= (5x)2 + (3y)2 + (2z)2 + 2(5x)(3y) + 2(3y)(2z) + 2(5x)(2z)
(5x + 3y + 2z)2 = 25x2 + 9y2 + 4z2 + 30xy + 12yz + 20xz
So, the expansion of (5x + 3y + 2z)2 is
25x2 + 9y2 + 4z2 + 30xy + 12yz + 20xz
Problem 2 :
If a + b + c = 15 , ab + bc + ac = 25, then find the value of
a2 + b2 + c2
Solution :
To get the value of (a2 + b2 + c2), we can use the formula or expansion of (a + b + c)2.
Write the formula / expansion for (a + b + c)2.
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ac)
Substitute 15 for (a + b + c) and 25 for (ab + bc + ac).
(15)2 = a2 + b2 + c2 + 2(25)
225 = a2 + b2 + c2 + 50
Subtract 50 from each side.
175 = a2 + b2 + c2
So, the value of a2 + b2 + c2 is 175.
Problem 3 :
Expand :
(x + 2y - z)2
Solution :
(x + 2y - z)2 is in the form of (a + b - c)2
Comparing (a + b - c)2 and (x + 2y - z)2, we get
a = x
b = 2y
c = z
Write the formula / expansion for (a + b - c)2.
(a + b - c)2 = a2 + b2 + c2 + 2ab - 2bc - 2ac
Substitute x for a, 2y for b and z for c.
(x + 2y - z)2 :
= x2 + (2y)2 + z2 + 2(x)(2y) - 2(2y)(z) - 2(x)(z)
(x + 2y - z)2 = x2 + 4y2 + z2 + 4xy - 4yz - 2xz
So, the expansion of (x + 2y - z)2 is
x2 + 4y2 + z2 + 4xy - 4yz - 2xz
Problem 4 :
Expand :
(3x - y + 2z)2
Solution :
(3x - y + 2z)2 is in the form of (a - b + c)2
Comparing (a + b - c)2 and (3x - y + 2z)2, we get
a = 3x
b = y
c = 2z
Write the formula / expansion for (a - b + c)2.
(a - b + c)2 = a2 + b2 + c2 - 2ab - 2bc + 2ac
Substitute 3x for a, y for b and 2z for c.
(3x - y + 2z)2 :
= (3x)2 + y2 + (2z)2 - 2(3x)(y) - 2(y)(2z) + 2(3x)(2z)
(3x - y + 2z)2 = 9x2 + y2 + 4z2 - 6xy - 4yz + 12xz
So, the expansion of (3x - y + 2z)2 is
9x2 + y2 + 4z2 - 6xy - 4yz + 12xz
Problem 5 :
Expand :
(x - 2y - 3z)2
Solution :
(x - 2y - 3z)2 is in the form of (a - b - c)2
Comparing (a - b - c)2 and (x - 2y - 3z)2, we get
a = x
b = 2y
c = 3z
Write the formula / expansion for (a - b - c)2.
(a - b - c)2 = a2 + b2 + c2 - 2ab + 2bc - 2ac
Substitute x for a, 2y for b and 3z for c.
(x - 2y - 3z)2 :
= x2 + (2y)2 + (3z)2 - 2(x)(2y) + 2(2y)(3z) - 2(x)(3z)
(x - 2y - 3z)2 = x2 + 4y2 + 9z2 - 4xy + 12yz - 6xz
So, the expansion of (x - 2y - 3z)2 is
x2 + 4y2 + 9z2 - 4xy + 12yz - 6xz
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