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y=4(x+3)2−8y=4(x+3)^2-8

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Full solution

Q. y=4(x+3)2−8y=4(x+3)^2-8
  1. Identify Expression: Identify the expression to be expanded.\newlineThe expression to be expanded is (x+3)2(x+3)^2, which is a binomial squared.
  2. Apply Binomial Square Formula: Apply the binomial square formula.\newlineThe binomial square formula is (a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2. Here, a=xa = x and b=3b = 3.\newlineSo, (x+3)2=x2+2×x×3+32(x+3)^2 = x^2 + 2\times x\times 3 + 3^2.
  3. Perform Multiplication: Perform the multiplication.\newlineNow we calculate each term: x2x^2, 2×x×3=6x2 \times x \times 3 = 6x, and 32=93^2 = 9.\newlineSo, (x+3)2=x2+6x+9(x+3)^2 = x^2 + 6x + 9.
  4. Multiply by 44: Multiply the expanded binomial by 44.\newlineWe have 4(x2+6x+9)4(x^2 + 6x + 9), which means we need to distribute the 44 to each term inside the parentheses.\newline4×x2=4x24\times x^2 = 4x^2, 4×6x=24x4\times 6x = 24x, and 4×9=364\times 9 = 36.\newlineSo, 4(x+3)2=4x2+24x+364(x+3)^2 = 4x^2 + 24x + 36.
  5. Subtract 88: Subtract 88 from the result of step 44.\newlineNow we have 4x2+24x+36−84x^2 + 24x + 36 - 8.\newlineSubtracting 88 from 3636 gives us 2828.\newlineSo, y=4x2+24x+28y = 4x^2 + 24x + 28.

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