Question

Expand each of the following using suitable identity: (i) (x+2y+4z)² (ii) ( 2x - y+z)² (iii) (-2x+3y+2z)² (iv) (3a-7b-c)² (v) (-2x+5y-3z)² (VI) (¼a - ½b + 1)²

Answer 1

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Answer 2

$\mathbb{ ANSWER }$ :

(i) (x+2y+4z)²

Using : (x+y+z)² = x² + y² + z² + 2xy + 2yz + 2xz
Here,
x = x , y = 2y , z = 4z

(x+2y+4z)² = (x)² + (2y)² + (4z)² + 2*x*2y + 2*2y*4z + 2*x*4z

= x² + 4y² + 16z² + 4xy + 16yz + 8xz

➖➖➖➖➖➖➖➖➖➖➖

(ii) ( 2x - y+z)²

Using : (x+y+z)² = x² + y² + z² + 2xy + 2yz + 2xz
Here,
x = 2x , y = (-y) , z = z

( 2x - y+z)² = (2x)² + (-y)² + (z)² + 2*2x*(-y) + 2*(-y) *z + 2*2x*z

= 4x² + y² + z² - 4xy - 2yz + 4xz

➖➖➖➖➖➖➖➖➖➖➖

(iii) (-2x+3y+2z)²

Using : (x+y+z)² = x² + y² + z² + 2xy + 2yz + 2xz
Here,
x = (-2x) , y = 3y , z = 2z

(-2x+3y+2z)² = (-2x)² + (3y)² + (2z)² + 2*(-2x)*3y + 2*3y*2z + 2*(-2x)*2z

= 4x² + 9y² + 4z² - 12xy + 12yz - 8xz

➖➖➖➖➖➖➖➖➖➖➖

(iv) (3a-7b-c)²

Using : (x+y+z)² = x² + y² + z² + 2xy + 2yz + 2xz
Here,
x = 3a , y = (-7b) , z = (-c)

(3a-7b-c)² = (3a)² + (-7b)² + (-c)² + 2*3a*(-7b) + 2*(-7b)*(-c) + 2*3a*(-c)

= 9a² + 49b² + c² - 42ab + 14bc - 6ac

➖➖➖➖➖➖➖➖➖➖➖

(v) (-2x+5y-3z)²

Using : (x+y+z)² = x² + y² + z² + 2xy + 2yz + 2xz
Here,
x = (-2x) , y = 5y , z = (-3z)

(-2x+5y-3z)² = (-2x)² + (5y)² + (-3z)² + 2*(-2x)*5y + 2*5y*(-3z) + 2*(-2x)*(-3z)

= 4x² + 25y² + 4z² - 20xy - 30yz + 12xz

➖➖➖➖➖➖➖➖➖➖➖

(VI) (¼a - ½b + 1)²

Using : (x+y+z)² = x² + y² + z² + 2xy + 2yz + 2xz
Here,
x = (¼a) , y = (-½b) , z = 1

(¼a - ½b + 1)² = (¼a)² + (-½b)² + (1)² + 2*¼a*(-½b) + 2*(-½b)*1 + 2*(¼a) *1

= 1/16 a² + 1/4 b² + 1 - 1/4 ab - b + 1/2 a

= a²/16 + b²/4 + 1 - (ab)/4 - b + a/2