Question

simplify. write each answer in standard form. (may need to foil or distribute)

1. (d - 2)(d + 9)
2. (5x + 7)^2
3. (2x - 3)(2x + 3)
4. (5a - 4b)(2a + 7b)
5. (3x - 2)(x^2 + 3x - 6)

find the perimeter of the triangle. write the answer in standard form.
15.
perimeter - add up the sides by combining like terms
find the area of the rectangle. write the answer in standard form.
16.
area - multiply length x width by foiling or distributing

Explanation:

Step1: Expand \((d - 2)(d + 9)\) using FOIL

$$
LATEXBLOCK0
$$

Step2: Combine like terms

$$ d^{2}+(9d-2d)-18=d^{2}+7d - 18 $$

Step3: Expand \((5x + 7)^{2}=(5x + 7)(5x + 7)\) using FOIL

$$
LATEXBLOCK1
$$

Step4: Combine like terms

$$ 25x^{2}+(35x+35x)+49=25x^{2}+70x + 49 $$

Step5: Expand \((2x - 3)(2x + 3)\) using the difference - of - squares formula \((a - b)(a + b)=a^{2}-b^{2}\) (where \(a = 2x\) and \(b = 3\))

$$ (2x)^{2}-3^{2}=4x^{2}-9 $$

Step6: Expand \((5a - 4b)(2a + 7b)\) using FOIL

$$
LATEXBLOCK2
$$

Step7: Combine like terms

$$ 10a^{2}+(35ab - 8ab)-28b^{2}=10a^{2}+27ab-28b^{2} $$

Step8: Expand \((3x - 2)(x^{2}+3x - 6)\) using the distributive property

$$
LATEXBLOCK3
$$

Step9: Combine like terms

$$ 3x^{3}+(9x^{2}-2x^{2})+(-18x-6x)+12=3x^{3}+7x^{2}-24x + 12 $$

Step10: Find the perimeter of the triangle with sides \(4x + 6\), \(3x-4\), and \(x - 3\)

$$
LATEXBLOCK4
$$

Step11: Find the area of the rectangle with length \(2x - 4\) and width \(x + 2\) using FOIL

$$
LATEXBLOCK5
$$

Answer:

1. \(d^{2}+7d - 18\)
2. \(25x^{2}+70x + 49\)
3. \(4x^{2}-9\)
4. \(10a^{2}+27ab-28b^{2}\)
5. \(3x^{3}+7x^{2}-24x + 12\)
6. \(8x-1\)
7. \(2x^{2}-8\)