Question

Q1. Using appropriate identity find the following products:
(3x2yz + 5)(3x2y + 7)​

Answer 1

Answer:

$(3 {x}^{2} yz + 5)(3 {x}^{2} y + 7) \\ \\ = (3 {x}^{2} yz + 5) \times 3 {x}^{2} y + (3 {x}^{2} yz + 5) \times 7 \\ \\ = 9 {x}^{4} {y}^{2} z + 15 {x}^{2} y + 21 {x}^{2} yz + 35 \\ \\ = 30 {x}^{2} yz + 15 {x}^{2} y + 35 \\ \\ = 5 ( 6x^2yz + 3 x^2y + 7 ) \\ \\= 6x^2yz + 3x^2y + 7$

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Answer 2

We need to expand (x+2y+4z)

2

We know appropriate identity (x+y+z)

2

=x

2

+y

2

+z

2

+2xy+2yz+2xz

Therefore, the value of (x+2y+4z)

2

is

=x

2

+(2y)

2

+(4z)

2

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

=x

2

+4y

2

+16z

2

+4xy+16yz+8xz

this is an example