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Question

Factorise: $$25a^{2}-4b^{2}+28bc-49c^{2}$$


Solution

$$25a^2-(4b^2-28bc+49c^2)$$ splitting middle term,
$$=25a^2-[4b^2-14bc-14bc+49c^2]$$
$$=25a^2-[2b(2b-7c)-7c(2b-7c)]$$
$$=25a^2-(2b-7c)^2=(5a)^2-(2b-7c)^2$$
$$=(5a+2b-7c)(5a-2b+7c)$$.

1208061_1395365_ans_1318d28a74464ee2a66b78c2b94ceeb5.jpg

Mathematics

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