Factoring Difference of Squares - Definition & Examples
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- A difference of two squares is an expression in the form x2−y2x^2 - y^2x2−y2. It expands to the expression (x+y)(x−y)(x + y)(x - y)(x+y)(x−y). When multiplying the two terms (x+…
By Vivian Loh, Alex Federspiel, Joshua Siktar, Jonathan Heller, Anusha Rahman
- Difference of Squares There's only one big thing you need to remember for this topic, and it's this equation: Notice that the left side of the equation above is literally the di…
By Hannah Bonville, Naomi Burgess, Alex Federspiel, Joshua Siktar, Jonathan Heller, Anusha Rahman, Caroline K
- (Video) The Difference of Squares by mathman1024 This by mathman1024 that shows how to employ the difference of squares method in factoring binomials. Summary\large{\text{Summar…
By Alex Federspiel, Naomi Burgess, Jonathan Heller, Anusha Rahman
Problems 34
- Factor 25x2−16y225x^2-16y^225x2−16y2.
- Factor the quadratic x2−16x^2 - 16x2−16.
- If U=x2−1U = x^2 -1U=x2−1 and V=x2+2x+1V = x^2 + 2x+1V=x2+2x+1, what is UUU divided by VVV? (Hint: It is a good idea to factor UUU and/or VVV before you divide.)
- The product (x+2)(x−2)(x+2)(x-2)(x+2)(x−2) is a factored form of which polynomial below?
- True or False\text{True or False}True or False === If a quadratic is in the form x2−cx^2-cx2−c where c>0c>0c>0, then you can always factor it into the product of (x+c)(x+\sqrt{c…
- What is a possible pair of factors for x2−169x^2-169x2−169? (Hint: To check your answer, multiply the factors together.)
- Let a,ba,ba,b be rational numbers. Which of the following statements are always true?
- Which of the following cannot be factored (over the integers) as a difference of perfect squares? (Factoring over the integers means factoring into polynomials of lower degree, …
- If a rectangle has side lengths of 3x+23x + 23x+2 and 3x−23x - 23x−2, what is the area of this rectangle?
- If a rectangle has an area of 16x4−916x^4 - 916x4−9, where x=2018x = 2018x=2018, what are its possible dimensions?
- What is a possible factorization of 4x2−34x^2 - 34x2−3?
- Which of the following is not a factored form of ab2−ac2ab^2 - ac^2ab2−ac2?
- What is not an equivalent way of writing (102−12)(10^2 - 1^2)(102−12)?
- Which of the following is an equivalent way of writing (2−4)(2 - 4)(2−4)?
- What is an equivalent way of writing 24−522^4 - 5^224−52?
- Write the following fraction in simplest form x4−y4x+y.\frac{x^4-y^4}{x+y}.x+yx4−y4.
- Simplify x2−1y2−1⋅y+1x+1.\frac{x^2-1}{y^2-1} \cdot \frac{y+1}{x+1}.y2−1x2−1⋅x+1y+1.
- Find ab2−4(b+2a2)\dfrac{a}{b^2-4} \left(\dfrac{b+2}{a^2}\right)b2−4a(a2b+2) in simplest form.
- What is ax2−by2ax^2 -by^2ax2−by2? Write it as the product of two binomials. (Here aaa and bbb are nonnegative real numbers.)
- What is 9x2−4y29x^2 - 4y^29x2−4y2?
- What is 162−12216^2-12^2162−122?
- We have two squares. One has area 100100100 square feet and the other one is 646464 square feet. What is the difference in areas, in square feet?
- Can you write 4x2−y24x^2 -y^24x2−y2 as the product of two binomials?
- What is the difference between 3452345^23452 and 2952295^22952?
- What is the difference of areas between the two gardens? Write the answer as the product of two binomials.
- Rewrite 81x2−25y281x^2-25y^281x2−25y2 as the product of two binomials.
- Simplify x2−5x+6x2−4÷x2+9−6xx2.\frac{x^2-5x+6}{x^2-4}\div \frac{x^2+9-6x}{x^2}.x2−4x2−5x+6÷x2x2+9−6x.
- Is x2−y2x^2-y^2x2−y2 divisible by x−yx-yx−y? If so, find the quotient.
- Which of the following are ways to write 4x2−44x^2 - 44x2−4 as the product of two binomials? Select all that apply. (Hint: You can check a factorization by expanding it.)
- Write the following polynomial as the product of a sum and difference: −4x2−25-4x^2-25−4x2−25
- Write the following polynomial as the product of a sum and difference: −x2+4-x^2+4−x2+4
- How can we re-write 13×713\times 713×7 so that we can use the shortcut of product of a sum and difference?
- Find the largest integer nnn such that n−2016n-2016n−2016 divides n2−2016n^2-2016n2−2016. Source: Lexington Math Tournament.
- Factor x2+10x−y2−2y+24x^2 + 10x - y^2 - 2y + 24x2+10x−y2−2y+24.