Multiply Binomials with FOIL Method - Examples & Practice
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- FOIL What a strange title. Aluminum foil, tin foil, what do those things have to do with mathematics? Well, FOIL is a nice way to remember how to multiply binomials. It will als…
By Freya Edholm, Po-Shen Loh, Moor Xu, Naomi Burgess, Jonathan Heller, Caroline K
- Using FOIL to Multiply Binomials In an earlier lesson, we saw how to multiply binomials using tables. Here, we're going to use the FOIL method! When multiplying binomials (expre…
By Hannah Bonville, Naomi Burgess, Alex Federspiel, Jonathan Heller, Anusha Rahman
- (Video) The FOIL Method by mathman1024 This video by mathman1024 goes over some examples of polynomial multiplication. He goes over a few methods including the FOIL method. Summ…
By Alex Federspiel, Amy Feraco, Jonathan Heller, Anusha Rahman, Caroline K
Problems 29
- Expand using FOIL and simplify (x2+x)(5x−1)(x^2+x)(5x-1)(x2+x)(5x−1). Write your answer in standard form.
- Expand (x+2)(x−3)(x+2)(x-3)(x+2)(x−3).
- Multiply (x6−x2)(x3−x)(x^6 - x^2)(x^3 - x)(x6−x2)(x3−x).
- What is the quadratic term, ax2ax^2ax2?
- What is the constant term, ccc?
- Find PQPQPQ, where P=x2+10P = x^2+10P=x2+10 and Q=x3−10Q = x^3 - 10Q=x3−10.
- Simplify by distributing. (−5x−6)(4x−9)(-5x-6)(4x-9)(−5x−6)(4x−9)
- Let a,b,c,da,b,c,da,b,c,d be real numbers so that when we FOIL out the expression (ax+b)(cx+d)(ax+b)(cx+d)(ax+b)(cx+d), we get a linear expression rather than a quadratic. Which…
- Let a,ba,ba,b be real numbers so that (ax+3)(bx+5)=24x2+42x+15(ax+3)(bx+5) = 24x^2 + 42x + 15(ax+3)(bx+5)=24x2+42x+15. Which of the following is a possible set of values for aaa…
- Let f(x)=5x+3f(x) = 5x + 3f(x)=5x+3 and g(x)=x−2g(x) = x - 2g(x)=x−2. What is f(x)×g(x)?f(x)\times g(x)?f(x)×g(x)?
- Which of the following is not part of "FOIL"?
- What are the outer terms in (3x+2)(x−4)(3x + 2)(x - 4)(3x+2)(x−4)?
- What is the product of the last terms in (x+3)(2x+1)(x + 3)(2x + 1)(x+3)(2x+1)?
- Which of the following is not a step in foiling (4x+2)(5x−1)(4x + 2)(5x - 1)(4x+2)(5x−1)?
- Which of the following is not a step in foiling (x3−2x)(3x2+1)(x^3 - 2x)(3x^2 + 1)(x3−2x)(3x2+1)?
- Simplify (2−r)(3+3r)(2 - r)(3 + 3r)(2−r)(3+3r) by foiling.
- If f(x)=3x+2f(x) = 3x + 2f(x)=3x+2, and g(x)=7x−1g(x) = 7x - 1g(x)=7x−1, what is (f∗g)(2)(f*g)(2)(f∗g)(2)?
- If a cylinder has a base with an area of 2x−42x - 42x−4, and a height of 3x+13x + 13x+1, what is its volume?
- Simplify (2x3−3x)(x+1)(2x^3 - 3x)(x + 1)(2x3−3x)(x+1) using the FOIL method.
- When is it best to use the FOIL method?
- What was the dimension of the lasagna before he changed it?
- Simplify the following expression: 3(3a+b)23(3a+b)^23(3a+b)2
- 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.)
- x2+kx+c=(x+a)(x+b)x2+kx+c=0\begin{array}{rcl} x^2 + kx + c &=& (x+a)(x+b) \\ x^2 + kx + c &=& 0 \end{array}x2+kx+cx2+kx+c==(x+a)(x+b)0 If kkk and ccc are defined constants, w…
- A triangle has a base of 2x−12x-12x−1 and a height of 6x−x26x-x^26x−x2. What is the area of this triangle if area equals one half the base times the height?
- Expand (x−1)(6x+y)(x-1)(6x+y)(x−1)(6x+y).
- Expand (3x+2)(5−8x2)(3x+2)(5-8x^2)(3x+2)(5−8x2) and sum the coefficients of each term. Take into account negatives and the fact that no coefficient in front of a term means 1.
- Expand (x+8)(2x−2)(x+8)(2x-2)(x+8)(2x−2) and sum the coefficients of each term. Take into account negatives and the fact that no coefficient in front of a term means 1.
- 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)