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rewrite each of the following expressions in expanded form. all of your answers should be in the form ( ax^2 + bx + c ) for numbers ( a, b, ) and ( c ).

a. ( (x + 1)(3x + 7) = ) input field with \3x^2+7\ (incorrect attempt) preview

b. ( (3x + 2)(4x + 8) = ) input field with \12x^2+2+16\ (incorrect attempt) preview

c. ( (x + 11)^2 = ) input field with \x^2+2+121\ (incorrect attempt) preview

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Explanation:

Part a: \((x + 1)(3x + 7)\)

Step1: Apply distributive property (FOIL)

Multiply \(x\) with \(3x\) and \(7\), then \(1\) with \(3x\) and \(7\):
\(x(3x) + x(7) + 1(3x) + 1(7)\)
\(= 3x^2 + 7x + 3x + 7\)

Step2: Combine like terms

Combine \(7x\) and \(3x\):
\(3x^2 + (7x + 3x) + 7 = 3x^2 + 10x + 7\)

Part b: \((3x + 2)(4x + 8)\)

Step1: Apply distributive property (FOIL)

Multiply \(3x\) with \(4x\) and \(8\), then \(2\) with \(4x\) and \(8\):
\(3x(4x) + 3x(8) + 2(4x) + 2(8)\)
\(= 12x^2 + 24x + 8x + 16\)

Step2: Combine like terms

Combine \(24x\) and \(8x\):
\(12x^2 + (24x + 8x) + 16 = 12x^2 + 32x + 16\)

Part c: \((x + 11)^2\)

Step1: Expand using \((a + b)^2 = a^2 + 2ab + b^2\)

Here, \(a = x\), \(b = 11\):
\(x^2 + 2(x)(11) + 11^2\)
\(= x^2 + 22x + 121\)

Answer:

s:
a. \(3x^2 + 10x + 7\)
b. \(12x^2 + 32x + 16\)
c. \(x^2 + 22x + 121\)