Multiplying a Difference of Squares - Definition & Examples
Read this topicExplanations 3
- Multiplying Matching Binomials What do we do when we want to multiply a pair of "matching" binomials (i.e. two binomials that happen to be the sum and difference of the same two…
By Hannah Bonville, Naomi Burgess, Alex Federspiel, Joshua Siktar, Jonathan Heller, Anusha Rahman
- (Video) Multiplying Binomial Conjugates by mathman1024 This video by mathman1024 covers multiplication with binomial conjugates. Summary\large{\text{Summary}}Summary A conjugate…
By Alex Federspiel, Christine, Joshua Siktar, Amy Feraco, Jonathan Heller, Anusha Rahman
- Difference of Squares with Geometry Can we understand this with geometry? Imagine two squares, an blue square with length of aaa and an orange square with side length of bbb. aa…
By Christine, Joshua Siktar, Amy Feraco, Jonathan Heller, Anusha Rahman
Problems 26
- What is 997×1003?997 \times 1003?997×1003? Write your answer without commas or spaces.
- The product (x+2)(x−2)(x+2)(x-2)(x+2)(x−2) is a factored form of which polynomial below?
- Expand the product (2x2+8)(2x2−8)(2x^2+8)(2x^2-8)(2x2+8)(2x2−8).
- A quadratic P(x)=ax2+bx+cP(x) = ax^2+bx+cP(x)=ax2+bx+c with integer coefficients has a zero at x=7+5x=7 + \sqrt{5}x=7+5. Find the product of the roots of PPP.
- Let a=1314a=\sqrt{\frac{13}{14}}a=1413. What is 121−a+121+a\frac{12}{1-a}+\frac{12}{1+a}1−a12+1+a12? Source: inspired by AIME 2016
- What is the product (x+6)(x−6)(x+6)(x-6)(x+6)(x−6)?
- What is the product (x+4)(x−2)?(x+4)(x-2)?(x+4)(x−2)?
- 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.)
- When expanding (2x+3)(2x−3)(2x + 3)(2x - 3)(2x+3)(2x−3), which terms cancel each other out?
- Which of the following is not a product of a sum and difference that allows cancellation of the linear term?
- What is (a+b)(a−b)(a + b)(a - b)(a+b)(a−b) when expanded and simplified?
- 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 (x+2)(x−2)(x + \sqrt{2})(x - \sqrt{2})(x+2)(x−2) when expanded and simplified?
- What is (ab+c)(ab−c)(\frac{a}{b} + c)(\frac{a}{b} - c)(ba+c)(ba−c) when expanded and simplified? (Note b≠0b \neq 0b=0)
- If 16=∣4−x∣∣4+x∣16 = |4-x||4+x|16=∣4−x∣∣4+x∣, find the smallest possible value of x2x^2x2.
- Write 205×195205\times 195205×195 as the difference of two squares.
- Simplify this expression: −(x−a)(x+a)+x2-(x-a)(x+a)+x^2−(x−a)(x+a)+x2
- Expand and simplify. (−3x−1)(3x−1)(-3x-1)(3x-1)(−3x−1)(3x−1)
- Expand and simplify. (10−3x)(10+3x)(10-3x)(10+3x)(10−3x)(10+3x)
- What should ??? be such that we can apply the formula (a+b)(a−b)=a2−b2(a+b)(a-b)=a^2 -b^2(a+b)(a−b)=a2−b2? (k+2)(k+?)(k+2)(k+?)(k+2)(k+?)
- Expand and simplify the following with FOIL as well as the product of a sum and difference; what term got canceled out? (2a+3b)(2a−3b)(2a+3b)(2a-3b)(2a+3b)(2a−3b)
- Expand: (2x2+y)(2x2−y)(2x^2 + y)(2x^2-y)(2x2+y)(2x2−y)
- What is (x−x2+42)(x+x2+42)(x-\sqrt{x^2+42})(x+\sqrt{x^2+42})(x−x2+42)(x+x2+42)?
- What is the product of (1+2x)(2x−1)(1+2x)(2x-1)(1+2x)(2x−1)?