simplify (5a+3b)^2 - (5a-3b)^2 .

asked by guest
on Mar 20, 2025 at 8:55 pm



You asked:

Simplify the expression: (5a+3b)2−(5a−3b)2{\left( 5 a + 3 b \right)}^{2} - {\left( 5 a - 3 b \right)}^{2}

MathBot Answer:

Simplified:

(5a+3b)2−(5a−3b)2=60ab {\left( 5 a + 3 b \right)}^{2} - {\left( 5 a - 3 b \right)}^{2} = 60 a b

(5a+3b)2−(5a−3b)2=9b2+25a2+30ab−(5a−3b)2=9b2+25a2+30ab−(−3b+5a)2=9b2+25a2+30ab−9b2+25a2−30ab=−25a2−9b2+30ab+9b2+25a2+30ab=60ab\begin{aligned}\left(5 a + 3 b\right)^{2} - \left(5 a - 3 b\right)^{2}&=9 b^{2} + 25 a^{2} + 30 a b - \left(5 a - 3 b\right)^{2}\\&=9 b^{2} + 25 a^{2} + 30 a b - \left(- 3 b + 5 a\right)^{2}\\&=9 b^{2} + 25 a^{2} + 30 a b - 9 b^{2} + 25 a^{2} - 30 a b\\&=- 25 a^{2} - 9 b^{2} + 30 a b + 9 b^{2} + 25 a^{2} + 30 a b\\&=60 a b\end{aligned}

Expanded:

(5a+3b)2−(5a−3b)2=60ab {\left( 5 a + 3 b \right)}^{2} - {\left( 5 a - 3 b \right)}^{2} = 60 a b

Factored:

(5a+3b)2−(5a−3b)2=60ab {\left( 5 a + 3 b \right)}^{2} - {\left( 5 a - 3 b \right)}^{2} = 60 a b


+ Submit Question