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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