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y=−9(x+1)(x+1)y=-9(x+1)(x+1)

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Full solution

Q. y=−9(x+1)(x+1)y=-9(x+1)(x+1)
  1. Use Distributive Property: We are given the quadratic expression y=−9(x+1)(x+1)y = -9(x + 1)(x + 1). To expand this, we will use the distributive property (also known as the FOIL method for binomials) to multiply the two binomials (x+1)(x + 1) and (x+1)(x + 1).
  2. Multiply First Terms: First, we multiply the first terms of each binomial: x×x=x2x \times x = x^2.
  3. Multiply Outer Terms: Next, we multiply the outer terms: x×1=xx \times 1 = x.
  4. Multiply Inner Terms: Then, we multiply the inner terms: 1×x=x1 \times x = x.
  5. Multiply Last Terms: After that, we multiply the last terms of each binomial: 1×1=11 \times 1 = 1.
  6. Combine Like Terms: Now, we combine like terms: x2+x+x+1=x2+2x+1x^2 + x + x + 1 = x^2 + 2x + 1.
  7. Multiply by −9 -9 : Finally, we multiply the entire expression by −9 -9 to get the expanded form: y=−9(x2+2x+1) y = -9(x^2 + 2x + 1) .
  8. Distribute −9-9: Distribute the −9-9 to each term in the binomial: y=−9×x2+(−9)×2x+(−9)×1y = -9 \times x^2 + (-9) \times 2x + (-9) \times 1.
  9. Perform Multiplication: Perform the multiplication: y=−9x2−18x−9y = -9x^2 - 18x - 9.

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