# Apply the distributive property to write an equivalent expression

Vignette In the Classroom In this vignette, students use associative, commutative, and distributive properties to generate equivalent algebraic expressions for the area of a rectangle. I already drew a picture to show what that might look like.

The first two questions face anyone who cares to distinguish the real from the unreal and the true from the false. The third question faces anyone who makes any decisions at all, and even not deciding is itself a decision.

Thus all persons practice philosophy whether they know it or not. Autocosmic Answers What is existing? Reality consists ultimately of matter and energy and their fundamentally lawlike and unwilled relations in space-time. To exist is to have a causal relationship with the rest of the universe.

The universe is the maximal set of circumstances that includes this statement and no subset of which is causally unrelated to the remainder. Humans do not know why the universe exists or what it is for.

The universe operates without supernatural intervention and according to lawlike regularities that can be understood through empirical investigation and without special intuition.

Humans have no credible evidence of any supernatural agency or unity. Humans have no credible evidence that any minds enjoy eternal existence. Knowledge is justified true belief. Truth is logical and parsimonious consistency with evidence and with other truth.

Meaning is the context-sensitive connotation ultimately established by relevant denotation and use. All synthetic propositions including this one can only be known from experience and are subject to doubt. A synthetic statement is propositionally meaningless if it is in principle neither falsifiable nor verifiable.

A mind is any volition al conscious faculty for perception and cognition. Minds and ideas consist ultimately of matter. Mental states are functional states consisting of causal relations among components for processing information.

Consciousness is awareness of self and environment. Intelligence is the ability to make, test, and apply inductions about perceptions of self and world. There are no forms of reasoning or kinds of knowledge that are in principle inaccessible to regular intelligence. As autonomous living intellects, we persons value intelligence and life and the autonomy they need to flourish.

A person is any intelligen t being with significant volitional control over how it affects other beings. All persons have the right to life and liberty. All beings have the right not to suffer torture or extinction.

Liberty is volition in the absence of aggression.

Aggression consists essentially of 1 coercion or 2 damage to a person's body, property, or rightful resources. Coercion is compulsion of one person by another through force or threat of aggression.

Justice is the minimization, reversal and punishment of aggression. The purpose of the state is to effect justice, provide aid and sustenance to persons in mortal danger, protect species in danger of extinction, and prevent torture.

Autocosmology is a synthesis of metaphysical naturalismontological materialismepistemological empiricism and positivismmental functionalismtheological atheismaxiological extropianismpolitical libertarianismeconomic capitalismconstitutional federalismbiological evolutionismevolutionary psychology, and technological optimism.

Autocosmology is the worldview asserted by this text. Human Answers Most humans justify their answers to philosophy's questions using one of four methods.

Faith is belief based on revelation and exempt from doubt. Mysticism is belief based on private and direct experience of ultimate reality. Skepticism is belief that is always subject to doubt and justified through objective verification.

Cynicism is the absence of belief. Faith is the most common mode of belief in the Western world, where the Abrahamic religions are prevalent. Mysticism is the most common mode of belief in the Eastern world. Skepticism is practiced worldwide with varying amounts of rigor by the minority of thinkers who have been influenced more by science than by tradition.

Cynicism too is practiced by a worldwide minority, often as a simplistic reaction to the rigidity of faith, the emptiness of mysticism, or the relativism of skepticism.

A skeptic believes what he sees. A mystic believes what he feels.§ Implementation of Texas Essential Knowledge and Skills for Mathematics, High School, Adopted (a) The provisions of §§ of this subchapter shall be . heartoftexashop.com Write expressions that record operations with numbers and with letters standing for numbers.

For example, express the calculation "Subtract y from 5" as 5 - y. Apply the properties of operations to generate equivalent expressions.

## Factoring Expressions (solutions, examples, worksheets, videos, lesson plans)

For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

Learn why the Common Core is important for your child. What parents should know; Myths vs. facts. We can instead write the expression as $$2\left (3p+5 \right)+\left (-1 \right)\left (p+2 \right)$$ By using the distributive property we can rewrite the expression as.

Practice applying the Distributive Property with these expressions. Expression Simplifying Calculator This calculator will simplify expressions, applying the distributive property when necessary. Next Lesson: FOIL Method Using the FOIL Method to multiply two or more parenthesis.

Chapter Subchapter C