Question

algebraic expressions review
name ____________________ date _______
examples problems

1. expand and simplify using foil

a) (s + 4)(s - 3) b) (2a - 5)(4a - 2)

1. a man’s lacrosse field has dimension of l = (3x + 18) and w = (2x - 5)

a) find an expression for the area of the field. (a = lw)
b) calculate the length, width, and area when x = 30 m

Explanation:

Step1: Recall FOIL Method

FOIL stands for First, Outer, Inner, Last. For \((a + b)(c + d)\), it's \(ac + ad + bc + bd\). Apply to \((s + 4)(s - 3)\).
First: \(s\times s = s^2\), Outer: \(s\times(-3)= -3s\), Inner: \(4\times s = 4s\), Last: \(4\times(-3)= -12\).

Step2: Combine Like Terms

Combine \(-3s\) and \(4s\): \(s^2 - 3s + 4s - 12 = s^2 + s - 12\).

Step3: Apply FOIL to \((2a - 5)(4a - 2)\)

First: \(2a\times4a = 8a^2\), Outer: \(2a\times(-2)= -4a\), Inner: \(-5\times4a = -20a\), Last: \(-5\times(-2)= 10\).

Step4: Combine Like Terms

Combine \(-4a\) and \(-20a\): \(8a^2 - 4a - 20a + 10 = 8a^2 - 24a + 10\).

Answer:

a) \(s^2 + s - 12\)
b) \(8a^2 - 24a + 10\)