Question

5. Factorise
o
25x2 + 16y2 + 47 – 40xy + 16yz - 20xz​

Answer 1

Step-by-step explanation:

$25 {x}^{2}+16{y}^{2}+ 4{z}^{2} - 40xy + 16yz - 20xz$

=

${( - 5x)}^{2} + ({4y})^{2} + {(2z)}^{2} + 2(( - 5x) \times 4y + 4y \times 2z + ( - 5x) \times 2z)$

=

${( - 5x + 4y + 2z)}^{2}$

Since,

${a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) = {(a + b + c)}^{2}$

=

$(4y - 5x + 2z)(4y - 5x + 2z)$

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Answer 2

Answer:

Step-by-step explanation:

Given 25x2 + 16y2 + 4z2 - 40xy + 16yz - 20xz

      = (−5x)2 + (4y)2 + (2z)2 + 2(−5x)(4y) + 2(4y)(2z) + 2(2z)(−5x)

It is in the form of [a2 + b2+ c2 + 2ab + 2bc + 2ca = (a + b + c)2]

      = [(−5x) + 4y +2z]2