![]() Since the square root of 81 is 9, Keith and Jasmine write 9 in the second place of each set of parentheses and plugged in the numbers into their solution, giving them (4x² + 9)(4x² - 9) = 0. The square root of 16 is 4 and the square root of 'x' to the fourth is 'x' squared, making the first term for each set of parentheses 4x squared. ![]() Now they just need to place the square root of each term of the binomial into the proper place. Keith and Jasmine set up the solution the way they were taught. Keith & Jasmine had to factor a doozey of a binomial when they got 16x⁴ - 81 = 0.īut they kept their cool and set up their solution. Since it's also possible that 'a' is negative and 'c' is positive, we could also see the binomial expression in the form c - ax² = 0. So let's change this plus to a minus, leaving us with ax² - c = 0. The coefficients 'a' and 'c' may not have the same sign. To be a difference of two squares, the 'b' coefficient must be 0 leaving us with ax² + c = 0. Let's start with a normal quadratic function: ax² + bx + c = 0. There were three critical points to the two teams' success. Phillip and Lara discuss the question and it looks like, yes, they do agree which is exactyl correct! Phillip and Lara win the square.and the GAME!!! Whew! that last round went quickly! Let's take a look at that again in slow motion. Dark Count, how do you factor this one? That's a tricky one, but the Dark Count looks confident and says the answer is (7 + x³)(7 - x³) = 0. The Dark Count’s question is 49 - x⁶ = 0. ![]() They're correct! And Keith & Jasmine win the square! What a block!īut Phillip and Lara can win the game here! Phillip and Lara pick the Dark Count’s square in hopes of ending this Bonus Round with a win. Keith & Jasmine take a moment to talk it over and yes!!! They agree with Rapunzel. Rapunzel says the answer is (4x² + 9)(4x² - 9) = 0. Okay, Rapunzel, your question is to factor 16x 4 - 81 = 0. They need a block, so they pick Rapunzel. They’re looking to come back from behind in this game. ![]() Now let’s join them in the bonus round already in progress. At last, just simplify the expressions and the equation is factored. Plug in the square root of the first term, x², in the first place in the parentheses and the root of the second term - disregard the minus sign - in the second place. Next, complete the parentheses with the square roots of the two terms from the binomial. Let’s see how they did it: First, set up your two factors like this: ( + )( - ) = 0. They were asked to solve x 2 - 64 = 0, which is the difference of two squares. They’re correct and get the square! And Round 1 goes to Phillip & Lara! Let’s take another look at the game-winning question. Evil says the answer is (x + 8)(x -8) = 0 and Phillip and Lara agree. Evil, the question is: How do you factor x 2 - 64 = 0? Dr. It’s time to play “The Difference of Two Squares”! Okay, it’s Phillip and Lara’s turn and they choose Dr. Welcome back! Let’s join our game, already in progress. Solve quadratic equations in one variable. Product of Sum and Difference of Two Squares: (a + b)( a – b) = a² – b²įactors of Difference of Two Squares: a² – b² = (a + b)(a – b) This method for factoring the difference of two squares can be represented in algebraic expressions as follows: To know more about this method for factoring the difference of two squares, you can watch this video. In other words, the factorization of 4x² – 25 = 0 is (2x + 5)(2x – 5) = 0, or (2x – 5)(2x + 5) = 0, as the commutative property of real numbers states that order of factors in multiplication or addition does not matter. Then 2x and 5 are the terms which appear in our product. When factoring such a difference of two squares, we end up always getting the product of the sum and the difference of the same two terms.įor instance, with 4x² – 25 = 0, we end up taking the square roots of 4x² and 25 to get 2x and 5, respectively. We will learn on how to factor the difference of two squares.
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