Question

Factorise 16 a square minus 25 B square minus 8 A plus one

Answer 1

$\texbf{Given:}$

$16a^2-25b^2-8a+1$

$=(16a^2-8a+1)-25b^2$

$=((4a)^2-2(4a)(1)+1^2)-25b^2$

$\text{Using the formula}$

$\boxed{\bf\,a^2-2ab+b^2=(a-b)^2}$

$=(4a-1)^2-(5b)^2$

$\text{Using the formula,}$

$\boxed{\bf\,a^2-b^2=(a-b)(a+b)}$

$\text{We can factorize}$

$=(4a-1-5b)(4a-1+5b)$

$\therefore\bf\,16a^2-25b^2-8a+1=(4a-1-5b)(4a-1+5b)$

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