Question

25a^2 - 4b^2 + 28bc -49^2

Answer 1

Answer:

Step-by-step explanation:

25a^2-4b^2+28bc-49c^2

=25a^2 -(2b^2+2 (2b)(7c)-7c^2

=25a^2-(2b-7c)^2

Formula=(a+b)(a-b)=a^2-b^2

=5a-(2b-7c)

=(5a+(2b-7c)(5a-(2b+7c)Answer

Answer 2

$\red{ \huge{ \underline { \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION \: \: \red{ \mid}}}}}}}}$


$\bold{25a {}^{2} - 4b {}^{2} + 28bc - 49c {}^{2} } \\ \\ \bold{ = 25a {}^{2} - (4b {}^{2} - 28bc + 49c {}^{2} ) \: \: \: - - - > (1) \: \: }$


$\underline{ \bold{ \: \: Use \: \: \underline{ \: \: (x - y) {}^{2} = x {}^{2} - 2xy + y {}^{2} \: \: } \: \: \: formula \: \: }}$
$\underline{ \bold{to \: \: simplify \: \: \underline{ \: \: 4b {}^{2} - 28bc + 49c {}^{2} \: }}}$


$\bold{4b {}^{2} - 28bc + 49c {}^{2} } \\ \\ \bold{ = (2b) {}^{2} - 2 \times 2b \times 7c + (7c) {}^{2} } \\ \\ \bold{ = (2b - 7c) {}^{2} }$


$\underline{ \bold{ \: \: \: \: So, \: \: \: \: \: \: (1) \: \: becomes \: \: \: \: }} \\ \\ \bold{25a {}^{2} - (4b {}^{2} - 28bc + 49c {}^{2}) } \\ \\ \bold{ = 25a {}^{2} - (2b - 7c) {}^{2} \: \:} \\ \\ \bold{ = (5a) {}^{2} - (2b - 7c) {}^{2} \: \: \: - - - > (2) \: \: }$


$\underline{ \bold{ \: \: \: Use \: \: \underline{\: \: x {}^{2} - y {}^{2} = (x + y)(x - y) \: \: } \: \:formula \: \: to \: \: \: }} \\ \underline{ \bold{ \: \: simplify \: \: (3) \: \: \: \: }}$

$\bold{(5a) {}^{2} - (2b - 7c) {}^{2} } \\ \\ \bold{ = (5a + (2b - 7c)(5a - (2b - 7c)} \\ \\ \bold{ = (5a + 2b - 7c)(5a - 2b + 7c)}$

$\bold{Hence,}$

$\boxed{ \boxed{ \bold{{25a {}^{2} - 4b {}^{2} + 28bc - 49c {}^{2} = (5a + 2b - 7c)(5a - 2b + 7c)}}}}$