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If (20 y+5)(4y-30)=80y^(2)+by-150 for all values of y where b is a constant, then which of the following is the value of b ? Choose 1 answer: (A) -580 (B) -40 (C) 0 (D) 620

If (20y+5)(4y−30)=80y2+by−150(20y+5)(4y-30)=80y^{2}+by-150 for all values of yy where bb is a constant, then which of the following is the value of bb?\newlineChoose 11 answer:\newline(A) −580-580\newline(B) −40-40\newline(C) 00\newline(D) 620620

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Full solution

Q. If (20y+5)(4y−30)=80y2+by−150(20y+5)(4y-30)=80y^{2}+by-150 for all values of yy where bb is a constant, then which of the following is the value of bb?\newlineChoose 11 answer:\newline(A) −580-580\newline(B) −40-40\newline(C) 00\newline(D) 620620
  1. Expand Equation: Expand the left side of the equation using the distributive property (FOIL method). \newline(20y+5)(4y−30)=20y(4y)+20y(−30)+5(4y)−5(30)(20y+5)(4y-30) = 20y(4y) + 20y(-30) + 5(4y) - 5(30)
  2. Simplify Expanded Form: Simplify the expanded form. 80y2−600y+20y−15080y^2 - 600y + 20y - 150
  3. Combine Like Terms: Combine like terms. 80y2−580y−15080y^2 - 580y - 150
  4. Compare with Right Side: Compare the simplified form with the right side of the given equation.\newline80y2−580y−150=80y2+by−15080y^2 - 580y - 150 = 80y^2 + by - 150
  5. Match Coefficients: Match the coefficients of the corresponding terms to find the value of bb.−580y=by-580y = by
  6. Conclude Value of b: Conclude that b=−580b = -580.

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