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Class 9MathematicsExploring Algebraic IdentitiesQuadratic expressionsMedium
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The length of a rectangular garden is \(x+4\) m and its breadth is \(x-2\) m. Which quadratic expression represents its area?

Answer and explanation

Correct answer: \(x^2+2x-8\)

Area of a rectangle = length × breadth. Thus, \((x+4)(x-2)=x^2-2x+4x-8=x^2+2x-8\). Option B has an incorrect middle term, \(6x\). Exam tip: multiply each term before combining like terms.

Related tags

Quadratic ExpressionsAlgebraic IdentitiesPolynomial MultiplicationRectangle AreaClass 9 MathematicsExploring Algebraic IdentitiesMathematicsClass 9 Mcq
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  1. 1Which expression can be factorised using the difference-of-cubes identity?
  2. 2What will be the factorised form of (r^2-2rs+s^2)?
  3. 3Which expression can be factorised directly using the identity for the difference of two squares?
  4. 4Which expression can be factorised directly using the difference-of-squares identity \(a^2-b^2=(a-b)(a+b)\)?
  5. 5Which expression is a quadratic expression?
  6. 6Based on the powers of the variable \(x\) in the polynomial \(5x^2-3x+7\), what is the degree of this expression?
  7. 7If a, b and c are constants, which condition is necessary for \(ax^2+bx+c\) to be a quadratic expression in x?
  8. 8If a quadratic expression has the general form \(ax^2+bx+c\), which condition on \(a\) is necessary for it to be quadratic?
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  10. 10Which of the following quadratic expressions can be factorised using the identity for the difference of two squares?
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