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Square of a Binomial

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Square of a Binomial

Study Guide

Key Definition

The square of a binomial $(a + b)^2$ or $(a - b)^2$ results in a trinomial.

Important Notes

The pattern for $(a + b)^2$ is $a^2 + 2ab + b^2$
The pattern for $(a - b)^2$ is $a^2 - 2ab + b^2$
A trinomial is a polynomial with three terms.
Perfect square trinomials can be factored back into binomials.
Use FOIL to verify binomial expansion.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

The square of a binomial results in a trinomial due to the distributive property, resulting in $a^2$, $2ab$, and $b^2$.

Remember

Remember the key formulas: $(a + b)^2 = a^2 + 2ab + b^2$, $(a - b)^2 = a^2 - 2ab + b^2$

Quick Reference

Pattern for $(a + b)^2$:$a^2 + 2ab + b^2$

Pattern for $(a - b)^2$:$a^2 - 2ab + b^2$

Understanding Square of a Binomial

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $(a+b)^2$ results in $a^2 + 2ab + b^2$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Expand $(x+3)^2$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A square garden with a side length of $(x+4)$ meters. What is the area?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Prove that $(2x-5)^2$ is equal to $4x^2 - 20x + 25$.

Challenge Quiz

Single Choice Quiz

Advanced

Which of the following is the expansion of $(3p - 2q^2)^2$?

Recap

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Review key concepts and takeaways