Algebraic Identities (1, 2, 3, 4, 5)

<p>The benevolent &quot;algebraicians&quot; have kindly bestowed upon us some slick shortcuts, known as &quot;identities.&quot;&nbsp;</p> <p>Identity 1: <strong>$ax + bx = x(a + b)$</strong></p> <ul> <li>$3x + 5x = x(3 + 5) = 8x$</li> <li>Factoring out the common factor is like gathering all the x&rsquo;s into one party.</li> </ul> <p>Identity 2: <strong>$ax - bx = x(a - b)$</strong></p> <ul> <li>$4x - 2x = x(4 - 2) = 2x$</li> <li>Same party trick, but with a bit of subtraction drama.</li> </ul> <p>Identity 3: <strong>$(a + b)^2 = a^2 + 2ab + b^2$</strong></p> <ul> <li>$(x + 3)^2 = x^2 + 2(x)(3) + 3^2 = x^2 + 6x + 9$</li> <li>The square of a binomial: turning a sum into a squared spectacle.</li> </ul> <p>Identity 4: <strong>$(a - b)^2 = a^2 - 2ab + b^2$</strong></p> <ol> <li>$(x - 4)^2 = x^2 - 2(x)(4) + 4^2 = x^2 - 8x + 16$</li> <li>The square of a difference: because subtraction deserves some flair too.</li> </ol> <p>Identity 5: <strong>$(a + b)(a - b) = a^2 - b^2$</strong></p> <ul> <li>$(x + 5)(x - 5) = x^2 - 5^2 = x^2 - 25$</li> <li>The difference of squares: when opposites attract and then subtract.</li> </ul> <p>These identities are your algebraic cheat codes, learn them well and use them wisely!</p>