which expression is equivalent to (5x -7)^2

Question

i need to find out which expression is equivalent to this problem

Answer 1

(5x-7)^2 is equivalent to (5x-7)(5x-7). The multiplication can be done using FOIL, which means the multiplication of the terms following the order of the First, the Outer, the Inner, and the Last. Therefore,

First: (5x)(5x) = 25x^2

Outer: (5x)(-7) = -35x

Inner: (-7)(5x) = -35x

Last: (-7)(-7) = 49

The result of the multiplication comes to 25x^2 - 70x +49 after combining like terms -35x(doubling it).

A faster way of the multiplication comes from realizing the Outer and the Inner multiplications yield the same product simply because the two expressions we are multiplying are the same. So whenever you are squaring a linear expression, a formula can be used: (ax+b)^2 = (ax)^2 + 2abx + b^2, and (ax-b)^2 = (ax)^2 - 2abx + b^2. So (5x-7)^2 = (5x)^2 - 2(5)(7)x + (7)^2 = 25x^2 - 70x +49.