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Simplify the following expression. {:[(4y+7)(y-2)],[4y^(2)+◻y+◻]:}

Simplify the following expression.\newline(4y+7)(y−2)4y2+□y+□ \begin{array}{l} (4 y+7)(y-2) \\ 4 y^{2}+\square y+\square \end{array}

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Full solution

Q. Simplify the following expression.\newline(4y+7)(y−2)4y2+□y+□ \begin{array}{l} (4 y+7)(y-2) \\ 4 y^{2}+\square y+\square \end{array}
  1. Expand binomials: To simplify the expression, we need to expand the numerator by multiplying the two binomials (4y+7)(4y+7) and (y−2)(y-2) using the distributive property (also known as the FOIL method for binomials).
  2. Multiply terms: First, multiply the first terms in each binomial: 4y×y=4y24y \times y = 4y^2.
  3. Combine like terms: Next, multiply the outer terms: 4y×(−2)=−8y4y \times (-2) = -8y.
  4. Simplify numerator: Then, multiply the inner terms: 7×y=7y7 \times y = 7y.
  5. Fill in denominator: Finally, multiply the last terms: 7×(−2)=−147 \times (-2) = -14.
  6. Fill in denominator: Finally, multiply the last terms: 7×(−2)=−147 \times (-2) = -14.Now, combine the like terms from the multiplication: 4y2+(−8y)+7y−144y^2 + (-8y) + 7y - 14.
  7. Fill in denominator: Finally, multiply the last terms: 7×(−2)=−147 \times (-2) = -14.Now, combine the like terms from the multiplication: 4y2+(−8y)+7y−144y^2 + (-8y) + 7y - 14.Combine the y terms: −8y+7y=−1y-8y + 7y = -1y.
  8. Fill in denominator: Finally, multiply the last terms: 7×(−2)=−147 \times (-2) = -14.Now, combine the like terms from the multiplication: 4y2+(−8y)+7y−144y^2 + (-8y) + 7y - 14.Combine the yy terms: −8y+7y=−1y-8y + 7y = -1y.The simplified form of the numerator is now 4y2−y−144y^2 - y - 14.
  9. Fill in denominator: Finally, multiply the last terms: 7×(−2)=−147 \times (-2) = -14.Now, combine the like terms from the multiplication: 4y2+(−8y)+7y−144y^2 + (-8y) + 7y - 14.Combine the y terms: −8y+7y=−1y-8y + 7y = -1y.The simplified form of the numerator is now 4y2−y−144y^2 - y - 14.The denominator is already given as 4y2+?y+□4y^2 + ?y + \square. We need to fill in the blanks with the corresponding terms from the simplified numerator.
  10. Fill in denominator: Finally, multiply the last terms: 7×(−2)=−147 \times (-2) = -14.Now, combine the like terms from the multiplication: 4y2+(−8y)+7y−144y^2 + (-8y) + 7y - 14.Combine the yy terms: −8y+7y=−1y-8y + 7y = -1y.The simplified form of the numerator is now 4y2−y−144y^2 - y - 14.The denominator is already given as 4y2+?y+□4y^2 + ?y + \square. We need to fill in the blanks with the corresponding terms from the simplified numerator.The term that corresponds to ?y?y in the denominator is −1y-1y from the numerator.
  11. Fill in denominator: Finally, multiply the last terms: 7×(−2)=−147 \times (-2) = -14.Now, combine the like terms from the multiplication: 4y2+(−8y)+7y−144y^2 + (-8y) + 7y - 14.Combine the y terms: −8y+7y=−1y-8y + 7y = -1y.The simplified form of the numerator is now 4y2−y−144y^2 - y - 14.The denominator is already given as 4y2+?y+□4y^2 + ?y + \square. We need to fill in the blanks with the corresponding terms from the simplified numerator.The term that corresponds to ?y?y in the denominator is −1y-1y from the numerator.The term that corresponds to □\square in the denominator is −14-14 from the numerator.

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