Question

$49x {}^{2} + 70xy + 25y {}^{2}$
​

Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{ \underline{ \mathcal{ \red {\: \: USING \: \: IDENTITY \: : \mapsto \: }}}} \\ \\ \underline{ \underline{ : \star : \: \: \bold{ IDENTITY \: \: USED \: : \star : }}} \\ \\ \: \: \: \: \: \: \: \: \boxed{ \mathtt{(a + b) {}^{2} = a{}^{2} + 2ab +b {}^{2} }} \\ \\ \\ \: \: \: \: \: \mathtt{49x {}^{2} + 70xy + 25y {}^{2} } \\ \\ \mathtt{ =(7x) {}^{2} + 2 \times (7x) \times (5y) + (5y) {}^{2} } \\ \\ \mathtt{ = (7x + 5y) {}^{2} } \\ \\ \mathtt{ = (7x + 5y)(7x + 5y)}$

$\huge{ \underline{ \underline{ \text{ \:OR, \: }}}}$

$\underline{ \underline{ \mathcal{ \red {\: \: SPILTTING \: \: OF \: \: MIDDLE \: \: TERM \: : \mapsto \: }}}} \\ \\ \: \: \: \: \: \mathtt{49x {}^{2} + 70xy + 25y {}^{2} } \\ \\ \mathtt{ = 49x {}^{2} + (35 + 35)xy + 25y {}^{2} } \\ \\ \mathtt{ = 49x {}^{2} + 35xy + 35xy + 25y {}^{2} } \\ \\ \mathtt{ = 7x(7x + 5y) + 5y(7x + 5y)} \\ \\ \mathtt{ = (7x + 5y)(7x + 5y)}$

Answer 2

$\huge\bold\red{Hey!}$

${49x}^{2} + 70xy + {25y}^{2} \\ {7x}^{2} + 2 \times 7x \times 5y + {5y}^{2} \\ {(7x + 5y)}^{2} \\ (7x + 5y)(7x + 5y)$