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  1. Asked: In:

    Factorise the following using appropriate identities: 9x² + 6xy + y²

    Best Answer
    bhoomi889

    (i) 9x² + 6xy + y² = (3x)² + 2 × 3x × y + y² = (3x + y)² [∵ a² + 2ab + b² = (a + b)]²

    (i) 9x² + 6xy + y²
    = (3x)² + 2 × 3x × y + y²
    = (3x + y)² [∵ a² + 2ab + b² = (a + b)]²

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  2. Asked: In:

    Factorise the following using appropriate identities: 4y² – 4y + 1

    Best Answer
    bhoomi889

    (ii) 4y² - 4y + 1 = (2y)² - 2 × 2y × 1 + 1² = (2y - 1)² [∵ a² - 2ab + b² = (a - b)²]

    (ii) 4y² – 4y + 1
    = (2y)² – 2 × 2y × 1 + 1²
    = (2y – 1)² [∵ a² – 2ab + b² = (a – b)²]

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  3. Asked: In:

    Factorise the following using appropriate identities: x²- y²/100

    bhoomi889

    (iii) x² - y²/100 = x² - (y/100)² = (x + y/100)(x - y/100) [∵ a² - b² = (a + b)(a - b)]

    (iii) x² – y²/100
    = x² – (y/100)²
    = (x + y/100)(x – y/100) [∵ a² – b² = (a + b)(a – b)]

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  4. Asked: In:

    Expand each of the following, using suitable identities: (x + 2y + 4z)²

    Best Answer
    bhoomi889

    (i) (x + 2y + 4z)² = x² + (2y)² + (4z)² + 2 × (x) × (2y) + 2 × (2y) × (4z) × (x) [∵ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca] = x² + 4y² + 16x² + 4xy + 16yz + 4zx

    (i) (x + 2y + 4z)²
    = x² + (2y)² + (4z)² + 2 × (x) × (2y) + 2 × (2y) × (4z) × (x) [∵ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca]
    = x² + 4y² + 16x² + 4xy + 16yz + 4zx

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  6. Asked: In:

    Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer. y² + √2.

    Best Answer
    bhoomi889

    y² + √2 Polynomials in one variable as it contains only one variable y.

    y² + √2 Polynomials in one variable as it contains only one variable y.

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