Question

factorise the 25x^2+16y^2+14z^2-40xy+16yz+20xz​

Answer 1

Step-by-step explanation:

Factorize

ANSWER

25x

2

+16y

2

+4z

2

−40xy+16yz−20xz

= (−5x)

2

+(4y)

2

+(2z)

2

+2(−5x)(4y)+2(4y)(2z)+2(−5x)(2z)

Suitable identities is (x+y+z)

3

=x

3

+y

3

+z

3

+2xy+2yz+2xz

Therefore, (−5x)

2

+(4y)

2

+(2z)

2

+2(−5x)(4y)+2(4y)(2z)+2(−5x)(2z)

= (−5x+4y+2z)

2

Answer 2

Step-by-step explanation:

$25 {x}^{2} + 16 {y}^{2} + 4 {z}^{2} - 40xy + 16yz + 20xz \\ = (5x {)}^{2} + (4y {)}^{2} + ( - 2z {)}^{2} - 2(5x \times 4y) - 2(4y \times - 2z) - 2(5x \times - 2z) \\ = (5x + 4y - 2z {)}^{2}$