Question

Solve 52*53 using algebraic identity

Answer 1

$$\begin{gathered} 52\times 53 \\ =\left(50+2\right)\left(50+3\right) \\ ={\left(50\right)}^2+\left(2+3\right)\left(50\right)+2\times 3 \\ =2500+5\times 50+6 \\ =2500+250+6 \\ =2756 \\ \boxed{\mathbf{Using}\mathbf{}\mathbf{identity}\mathbf{}\mathbf{:} \\ \left(\mathbf{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{a}\right)\left(\mathbf{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{b}\right)\mathbf{}\mathbf{=}\mathbf{}{\mathbf{x}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)\mathbf{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{ab}} \end{gathered}$$