factorise 25z²-x²-2x-1
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Answer:
(z+x+1)(z−x−1)
Step-by-step explanation:
\begin{gathered} {z}^{2} - {x}^{2} - 2x - 1 \\ \\ = {z}^{2} - ( {x}^{2} + 2x + 1) \\ \\ = {z}^{2} - \left[{(x)}^{2} + 2( x)(1) + {(1)}^{2} \right]\\ \\ = {z}^{2} - {(x + 1)}^{2} \\ \\ = ( z + x + 1)(z - x - 1)\end{gathered}
z
2
−x
2
−2x−1
=z
2
−(x
2
+2x+1)
=z
2
−[(x)
2
+2(x)(1)+(1)
2
]
=z
2
−(x+1)
2
=(z+x+1)(z−x−1)
Concept Map:-
{(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}(x+y)
2
=x
2
+2xy+y
2
{x}^{2} - {y}^{2} = (x + y)(x - y)x
2
−y
2
=(x+y)(x−y)
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