Question

geometry - lindemuth
foil method
find each product.

1. (3r + 5)(4r + 4)
2. (2b - 1)(4b - 4)
3. (3n - 2)(4n + 1)
4. (p - 2)(5p - 2)
5. (3n + 4)(3n + 3)
6. (3x - 4)(4x + 5)
7. (2n + 4)(5n + 4)
8. (2v - 4)(2v - 3)
9. (-6x + 1)(-5x - 1)
10. (2n - 8)(n - 2)

Explanation:

Step1: Recall FOIL method

FOIL stands for First - Outer - Inner - Last. For \((a + b)(c + d)=ac+ad+bc+bd\).

Step2: Solve (1) \((3r + 5)(4r + 4)\)

First: \(3r\times4r = 12r^{2}\), Outer: \(3r\times4=12r\), Inner: \(5\times4r = 20r\), Last: \(5\times4 = 20\). Then \(12r^{2}+12r + 20r+20=12r^{2}+32r + 20\).

Step3: Solve (2) \((2b-1)(4b - 4)\)

First: \(2b\times4b=8b^{2}\), Outer: \(2b\times(-4)=-8b\), Inner: \((-1)\times4b=-4b\), Last: \((-1)\times(-4) = 4\). Then \(8b^{2}-8b-4b + 4=8b^{2}-12b + 4\).

Step4: Solve (3) \((3n-2)(4n + 1)\)

First: \(3n\times4n=12n^{2}\), Outer: \(3n\times1 = 3n\), Inner: \((-2)\times4n=-8n\), Last: \((-2)\times1=-2\). Then \(12n^{2}+3n-8n-2=12n^{2}-5n-2\).

Step5: Solve (4) \((p - 2)(5p-2)\)

First: \(p\times5p=5p^{2}\), Outer: \(p\times(-2)=-2p\), Inner: \((-2)\times5p=-10p\), Last: \((-2)\times(-2)=4\). Then \(5p^{2}-2p-10p + 4=5p^{2}-12p + 4\).

Step6: Solve (5) \((3n + 4)(3n + 3)\)

First: \(3n\times3n=9n^{2}\), Outer: \(3n\times3 = 9n\), Inner: \(4\times3n=12n\), Last: \(4\times3 = 12\). Then \(9n^{2}+9n+12n+12=9n^{2}+21n+12\).

Step7: Solve (6) \((3x-4)(4x + 5)\)

First: \(3x\times4x=12x^{2}\), Outer: \(3x\times5 = 15x\), Inner: \((-4)\times4x=-16x\), Last: \((-4)\times5=-20\). Then \(12x^{2}+15x-16x-20=12x^{2}-x-20\).

Step8: Solve (7) \((2n + 4)(5n + 4)\)

First: \(2n\times5n=10n^{2}\), Outer: \(2n\times4 = 8n\), Inner: \(4\times5n=20n\), Last: \(4\times4 = 16\). Then \(10n^{2}+8n+20n+16=10n^{2}+28n+16\).

Step9: Solve (8) \((2v-4)(2v-3)\)

First: \(2v\times2v=4v^{2}\), Outer: \(2v\times(-3)=-6v\), Inner: \((-4)\times2v=-8v\), Last: \((-4)\times(-3)=12\). Then \(4v^{2}-6v-8v + 12=4v^{2}-14v + 12\).

Step10: Solve (9) \((-6x + 1)(-5x-1)\)

First: \((-6x)\times(-5x)=30x^{2}\), Outer: \((-6x)\times(-1)=6x\), Inner: \(1\times(-5x)=-5x\), Last: \(1\times(-1)=-1\). Then \(30x^{2}+6x-5x-1=30x^{2}+x-1\).

Step11: Solve (10) \((2n-8)(n - 2)\)

First: \(2n\timesn=2n^{2}\), Outer: \(2n\times(-2)=-4n\), Inner: \((-8)\timesn=-8n\), Last: \((-8)\times(-2)=16\). Then \(2n^{2}-4n-8n + 16=2n^{2}-12n + 16\).

Answer:

1. \(12r^{2}+32r + 20\)
2. \(8b^{2}-12b + 4\)
3. \(12n^{2}-5n-2\)
4. \(5p^{2}-12p + 4\)
5. \(9n^{2}+21n+12\)
6. \(12x^{2}-x-20\)
7. \(10n^{2}+28n+16\)
8. \(4v^{2}-14v + 12\)
9. \(30x^{2}+x-1\)
10. \(2n^{2}-12n + 16\)