Question

Multiply:

(x+y)by (x+y)
a+b by a^2-b^2
(a+5) by (a^2-2a-3)
(a^2-ab+b^3) by (a+b)​

Answer 1

Multiply:

`(x+y)by (x+y)`

`: \implies(x + y)(x + y)`

`: \implies \: x(x + y) + y(x + y)`

`: \implies {x}^(2) + xy + xy + {y}^(2)`

`: \implies{x}^(2) + 2xy + {y}^(2)`

Multiply:

`a+b \: by \: a^2-b^2`

`: \implies( {a}^(2) + {b}^(2) ) * (a + b)`

`: \implies \: {a}^(2) (a + b) - {b}^(2) (a + b)`

`: \implies \: {a}^(3) + {a}^(2) b - {ab}^(2) - {b}^(3)`

Multiply:

`(a+5) by (a^2-2a-3)`

`: \implies{(a + 5) * ( {a}^(2) - 2a - 3) }`

`: \implies \: a({a}^(2) - 2a - 3) + 5( {a}^(2) - 2a - 3)`

`: \implies(a * {a}^(2) - a * 2a - a * 3) + (5 * {a}^(2) - 5 * 2a - 5 * 3)`

`: \implies{a}^(3) - {2a}^(2) - 3a + 5 {a}^(2) - 10a - 15`

`: \implies{ {a}^(3) + {3a}^(2) - 13a - 15}`

Multiply:

`(a^2-ab+b^3) by (a+b)`

`: \implies{(a + b) * ( {a}^(2) - ab + {b}^(3) )}`

`: \implies \: a( {a}^(2) - ab + {b}^(3)) + b( {a}^(2) - ab + {b}^(3) )`

`: \implies {a}^(3) - {a}^(2) b + a {b}^(3) + {a^2b} - {ab}^(2) + {b}^(4)`

`: \implies{ {a}^(3)+ab^3 - ab^2+ {b}^(4) }`

Explanation:

`\blue{ \frak{Seolle_(aph.rodite)}}`