Question

please solve it -

Factorise the following bionomials-

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Answer 1

16:-

$\frac{36 m^2}{289} - 81$

= $\frac{(6m)^2}{(17)^2} - (9)^2$

= $(\frac{6m}{17})^2 - (9)^2$

∵ $a^2 - b^2 = (a + b)(a - b),$

= $\boxed{(\frac{6m}{17} + 9)(\frac{6m}{17} - 9) }$

20:-

$81 - (x - 7)^2$

= $(9)^2 - (x - 7)^2$

∵ $a^2 - b^2 = (a + b)(a - b),$

= $[(9) + (x - 7)][(9) - (x - 7)]$

= $(9 + x - 7)(9 - x + 7)$

= $\boxed{ (2 + x)(16 - x)}$

More identities for you:-

• $(a + b)^2 = a^2 + 2ab + b^2$
• $(a - b)^2 = a^2 - 2ab + b^2$
• $(x + a)(x + b) = x^2 + (a + b)x + ab$
• $(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)$
• $(a + b)^3 = a^3 + b^3 + 3ab(a + b)$
• $(a - b)^3 = a^3 - b^3 - 3ab(a - b)$
• $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$
• $4ab = (a + b)^2 - (a - b)^2$
• $2(a^2 + b^2) = (a + b)^2 + (a - b)^2$
• $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$
• $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$.

There are many such identities. Keep on exploring and utilising.