Question

multiply the polynomials by algebraic theorem or chians teaching method:
14 ((4x - 2)(3 - x))
15 ((x^2 + 2x)(3x^2 + x))

Explanation:

Problem 14: \((4x - 2)(3 - x)\)

Step 1: Apply the distributive property (FOIL method)

Multiply the First terms: \(4x \times 3 = 12x\)
Multiply the Outer terms: \(4x \times (-x) = -4x^2\)
Multiply the Inner terms: \(-2 \times 3 = -6\)
Multiply the Last terms: \(-2 \times (-x) = 2x\)

Step 2: Combine like terms

Combine the \(x\)-terms: \(12x + 2x = 14x\)
Now, write all terms together: \(-4x^2 + 14x - 6\)

Problem 15: \((x^2 + 2x)(3x^2 + x)\)

Step 1: Apply the distributive property (FOIL method for polynomials)

Multiply \(x^2\) by each term in the second polynomial:
\(x^2 \times 3x^2 = 3x^4\)
\(x^2 \times x = x^3\)

Multiply \(2x\) by each term in the second polynomial:
\(2x \times 3x^2 = 6x^3\)
\(2x \times x = 2x^2\)

Step 2: Combine like terms

Combine the \(x^3\)-terms: \(x^3 + 6x^3 = 7x^3\)

Now, write all terms together: \(3x^4 + 7x^3 + 2x^2\)

Answer:

s:

1. \(\boldsymbol{-4x^2 + 14x - 6}\)
2. \(\boldsymbol{3x^4 + 7x^3 + 2x^2}\)