a^4-25b^2+30b-9, factorise
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4a2−(25b2−30b+9)
\mathsf{=4a^2-((5b)^2-2{\times}5b{\times}3+3^2)}=4a2−((5b)2−2×5b×3+32)
\textsf{Using identity (1),}Using identity (1),
\mathsf{=4a^2-(5b-3)^2}=4a2−(5b−3)2
\mathsf{=(2a)^2-(5b-3)^2}=(2a)2−(5b−3)2
\textsf{Using identity (2),}Using identity (2),
\mathsf{=(2a-(5b-3))\,(2a+5b-3)}=(2a−(5b−3))(2a+5b−3)
\mathsf{=(2a-5b+3)\,(2a+5b-3)}=(2a−5b+3)(2a+5b−3)
\implies\boxed{\mathsf{4a^2-25b^2+30b-9=(2a-5b+3)\,(2a+5b-3)}}⟹4a2−25b2+30b−9=(2a−5b+3)(2a+5b−3)
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