Examkin

Soru

Zorluk: KolayMultiplying Polynomials

What is the product of the binomials (2x−1)(2x - 1) and (x+4)(x + 4)?

  1. A
    2x2−42x^2 - 4
  2. B
    2x2−7x−42x^2 - 7x - 4
  3. 2x2+7x−42x^2 + 7x - 4Cevap
  4. D
    9x3−49x^3 - 4

Cevap

The correct expression is 2x2+7x−42x^2 + 7x - 4.
By applying the FOIL method, we multiply the First terms to get 2x22x^2, the Outer terms to get 8x8x, the Inner terms to get −x-x, and the Last terms to get −4-4. Combining the like terms 8x8x and −x-x results in the simplified polynomial 2x2+7x−42x^2 + 7x - 4.

Adım Adım Çözüm

1
Multiply the First terms.
2x×x=2x22x \times x = 2x^2
This is the 'F' step in the FOIL method.
2
Multiply the Outer terms.
2x×4=8x2x \times 4 = 8x
This is the 'O' step in the FOIL method.
3
Multiply the Inner terms.
−1×x=−x-1 \times x = -x
This is the 'I' step in the FOIL method.
4
Multiply the Last terms.
−1×4=−4-1 \times 4 = -4
This is the 'L' step in the FOIL method.
5
Combine the resulting terms.
2x2+8x−x−4=2x2+7x−42x^2 + 8x - x - 4 = 2x^2 + 7x - 4
Combine the like middle terms (8x8x and −x-x) to simplify the final expression.

Anahtar Kavram

Multiplying binomials using the distributive property (FOIL method) and combining like terms.
Bu soruyu puanla

Konular

Multiplying Polynomials

Bu konudan daha fazla soru