Question

proving (a + b)^2 = a^2 +2ab + b^2

do this as a two column proof

Hint: (a + b)2 = (a + b)(a + b) may be a good way to get started. You can then do more algebra steps to the (a + b)(a + b) expression to eventually re-write it as a2 + 2ab + b2 .

Answer 1

yes this is solved by the distributive property of multiplication.

${(a + b)}^{2} = (a + b)(a + b)$

$= {a}^{2} + ab + {b}^{2} + ab$

${a}^{2} + 2ab + {b}^{2}$

therefore

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$