箔法
FOIL 公式用于执行两个二项式之间的乘法运算。二项式是只有两项的多项式。示例：x+3、x 2 +4、5x 2 +3x。二项式是包含常数、变量、指数和系数的 2 项代数表达式。 FOIL 中的每个字母代表两个二项式相乘的步骤。
FOIL stands for-
F-First-> First terms in each binomial are multiplied with each other.
O-Outer-> Outer terms of binomials are multiplied with each other.
I-Inner-> Inner terms of binomials are multiplied.
L-Last-> Last term in each binomial is multiplied by each other.
FOIL公式的标准形式是
(a+b) × (c+d) = ac + ad + bc + bd
Where two binomials are a+b, c+d
a, c are first terms
a, d are outer terms in each binomial
b, c are inner terms
b, d are last terms of binomials.
Note: While multiplying terms, if bases are same then add their exponents to get result.
示例问题
问题 1：使用FOIL 公式将两个二项式 6x+2 和 3x+8 相乘。
解决方案：
Given binomials,
(6x+2), (3x+8)
FOIL Formula
(a+b) × (c+d) = ac+ad+bc+bd
(6x+2) × (3x+8) = (6x×3x)+(6x×8)+(2×3x)+(2×8)
= 18x2+48x+6x+16
= 18x2+54x+16
Multiplication between 6x+2 and 3x+8 is 18x2+54x+16
问题 2：使用 FOIL 公式将两个二项式 x+2 和 3x-3 相乘。
解决方案：
Given binomials,
(x+2), (3x-3)
FOIL Formula
(a+b)x(c+d) = ac+ad+bc+bd
(x+2)×(3x-3) = (x×3x)+(x×(-3))+(2×3x)+(2×(-3))
= 3x2-3x+6x-6
= 3x2+3x-6
Multiplication between x+2 and 3x-3 is 3x2+3x-6
问题 3：使用FOIL 公式将两个二项式 2x 2 +1 和 3x+1 相乘。
解决方案：
Given binomials,
(2x2+1), (3x+1)
FOIL Formula
(a+b)x(c+d) = ac+ad+bc+bd
(2x2+1)×(3x+1) = (2x2×3x)+(2x2×1)+(1×3x)+(1×1)
= 6x3+2x2+3x+1
Multiplication between 2x2+1 and 3x+1 is 6x3+2x2+3x+1
问题 4：使用FOIL 公式将两个二项式 4x 2 -2 和 x 2 +4 相乘。
解决方案：
Given binomials,
(4x2-2), (x2+4)
FOIL Formula
(a+b)x(c+d) = ac+ad+bc+bd
(4x2-2)×(x2+4) = (4x2×x2)+(4x2×4)+(-2×x2)+(-2×4)
= 4x4+16x2-2x2-8
= 4x4+14x2-8
Multiplication between 4x2-2 and x2+4 is 4x4+14x2-8
问题 5：如果我们将两个二项式 t+1 和 t+2 相乘，结果是什么。 （应用 FOIL 公式）
解决方案：
Given binomials,
(t+1), (t+2)
FOIL Formula
(a+b)×(c+d)=ac+ad+bc+bd
(t+1)×(t+2) = (t×t)+(t×2)+(1×t)+(1×2)
= t2+2t+t+2
= t2+3t+2
Multiplication between t+1 and t+2 is t2+3t+2