What I learned this week (Polynomials)

I learned FOIL (First, outer, inner, last)

FOIL is a way to multiply binomials and utilize the distributive property.

Take this expression for example: $(4x + 3)(2x + 5)$

The F is for first, which is multiplying the first term in each binomial.

$4x \cdot 2x = 8x^2$

The O is for outer, which is multiplying the outer or the first and last terms of the whole equation.

$4x \cdot 5 = 20x$

The I is for inner, which is multiplying the inner or the second and third terms of the whole equation.

$3 \cdot 2x = 6x$

The L is for last, which is multiplying the last term in each binomial.

$3 \cdot 5 = 15$

You will then have each of those in an addition expression.

$8x^2 + 20x + 6x + 15$

Simplify where you can.

$8x^2 + 26x + 15$

That is the process of FOIL, which is an easy way to understand and use the distributive property with binomials.

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