Question

$\text{Factorise:}25+70x+49x^2$

• A. $(5x+7)(5x+2)$
• B. $(7x+5)(5x+3)$
• C. $(7x+5)(7x+5)$
• D. $(3x+7{)}^2$

Answer 1

The correct option is C

$(7x+5)(7x+5)$

The given expression can be rewritten as,
$49x^2+70x+25$

$\text{Using the identity:}(a+b{)}^2=a^2+2ab+b^2,\text{we get}$

$49x^2+70x+25=(7x{)}^2+2(5\left)\right(7x)+5^2$
$=(7x+5{)}^2$​
$=(7x+5)(7x+5)$

$\therefore 25+70x+49x^2=(7x+5)(7x+5)$