Difference or Sum of Squares with Complex Numbers
Read this topicExplanations 7
- So as to not get a headache and deal with complex numbers, we shall let c≥0c\geq 0c≥0 for the equation x2−c=0x^{2}-c =0x2−c=0. Now we define a new variable d=cd = \sqrt{c}d=c. …
By Winston Ou, Victor Wang
- We can use the difference of two squares method of factoring to multiply numbers that have an even difference. This works because of the following algebraic equation: x2−y2=(x−y…
By Stefan Cuevas, Naomi Burgess
- (Video) Difference of Squares Multiplication by Mr. T's Math Videos This video by YouTube channel Mr T's Math Videos shows how to multiply two numbers using the difference of sq…
By Stefan Cuevas, Naomi Burgess, Alex Federspiel
- (Video) Multiplying Surds by HEGARTYMATHS Here's a good video by HEGARTYMATHS showing you how to quickly multiply two binomials together if they are of the form (a+b)(a−b)(a+b)(…
By Alex Federspiel, Naomi Burgess, Joshua Siktar
- (Video) Factoring Differences of Squares by yaymath Here's a video by yaymath that shows you how to factor a difference of squares (a polynomial that is in the form of A2−B2A^2-…
By Alex Federspiel, Naomi Burgess
- (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
- Sum and Difference of Squares The difference of squares is a method for factoring certain kinds of binomials. Let's do a quick review of this method before we dive a little bit …
By Jonathan Heller
Problems 26
- Factor the expression x4−1x^4 - 1x4−1.
- Factor the quadratic x2−2x^2 - 2x2−2.
- What is 997×1003?997 \times 1003?997×1003? Write your answer without commas or spaces.
- Which of the following polynomials can be factored (into linear polynomials with integer coefficients) using the knowledge that they are a difference of two perfect squares?
- Using the difference of squares method of multiplication, find the product: 100×20100 \times 20100×20. Your answer should NOT include commas or spaces.
- What is the midpoint (average) of 353535 and 55?55?55?
- Which of the following numbers can be multiplied easily using the difference of squares method? You can choose more than one.
- Which of the following is a factor of the binomial 6400x20−646400x^{20} - 646400x20−64?
- What is 26×2426 \times 2426×24? (Use difference of two squares to multiply these.)
- Find a value of nnn satisfying 20152+n=201722015^2 + n = 2017^220152+n=20172.
- Evaluate 100022522−2482\frac{1000^2}{252^2 - 248^2}2522−248210002.
- How many different lines does the graph of x4=x2y2x^4 = x^2y^2x4=x2y2 contain? Source: Alex Zhu, Problems of the Week 1, 2012
- Find the smallest solution of the equation x4−25x2+144=0x^4 - 25x^2 + 144 = 0x4−25x2+144=0.
- Let x,y,zx,y,zx,y,z be positive real numbers such that y2−x2=9y^2 - x^2 = 9y2−x2=9, z2−y2=11z^2 - y^2 = 11z2−y2=11, and x+y+z=15.x+y+z = 15.x+y+z=15. What is 100x+10y+z?100x+10y…
- Let x,y,zx,y,zx,y,z be positive integers such that y2−x2=99y^2 - x^2 = 99y2−x2=99 and z2−y2=101z^2 - y^2 = 101z2−y2=101. What is yyy? Note: 101101101 is prime. Source: inspired …
- The number 104,060,465104{,}060{,}465104,060,465 is divisible by a five-digit prime number. What is that prime number? (Hint: Do the digits look like a row of Pascal's triangle?…
- Let a,ba,ba,b be real numbers. Which of the following statements are always true?
- Factor the quadratic: x4−49x^4-49x4−49
- How many integers between 1 and 1000 can be expressed as the difference of two perfect squares? (AIME)
- Let xxx and yyy be two-digit integers such that yyy is obtained by reversing the digits of xxx. The integers xxx and yyy satisfy x2−y2=m2x^2 - y^2 = m^2x2−y2=m2 for some positiv…
- Expand (a−b)(a+b)3−2ab(a2−b2)(a-b)(a+b)^3-2ab(a^2-b^2)(a−b)(a+b)3−2ab(a2−b2).
- What is 14×614 \times 614×6 using the difference of squares formula?
- If Joanna has 171717 buckets, and each bucket contains 555 bananas, how many bananas does Joanna have in total?
- What is ax2−by2ax^2 -by^2ax2−by2? Write it as the product of two binomials. (Here aaa and bbb are nonnegative real numbers.)
- Write 511×489511\times 489511×489 as the difference of two squares.
- Write the following polynomial as the product of a sum and difference: −x2+4-x^2+4−x2+4