Answer :

_{i.}_{(a + b)(a – b)(a}^{2} + ab + b^{2})(a^{2} – ab + b^{2})

= (a + b)(a^{2} – ab + b^{2})(a – b)(a^{2} + ab + b^{2})

Using x^{3} – y^{3} = (x – y)(x^{2} + xy + y^{2})

x^{3} + y^{3} = (x + y)(x^{2} – xy + y^{2})

= (a^{3} + b^{3})(a^{3} – b^{3})

Now, using (a + b)(a – b) = a^{2} – b^{2}

= a^{6} – b^{6}

**ii.** (a – 2b)(a^{2} + 2ab + 4b^{2})(a^{3} + 8b^{3})

= (a – 2b)(a^{2} + a(2b) + (2b)^{2})(a^{3} + (2b)^{3})

Using x^{3} – y^{3} = (x – y)(x^{2} + xy + y^{2})

x^{3} + y^{3} = (x + y)(x^{2} – xy + y^{2})

= (a^{3} – (2b)^{3})(a^{3} + (2b)^{3})

Now, using (a + b)(a – b) = a^{2} – b^{2}

= a^{6} – (2b)^{6}

= a^{6} – 64b^{6}

**iii.** (4a^{2} – 9)(4a^{2} – 6a + 9)(4a^{2} + 6a + 9)

= [(2a)^{2} – 3^{2}](4a^{2} – 6a + 9)(4a^{2} + 6a + 9)

Using x^{2} – y^{2} = (x – y)(x + y)

= (2a – 3)(2a + 3)(4a^{2} – 6a + 9)(4a^{2} + 6a + 9)

= (2a – 3)(4a^{2} + 6a + 9)(2a + 3)(4a^{2} – 6a + 9)

Using x^{3} – y^{3} = (x – y)(x^{2} + xy + y^{2})

x^{3} + y^{3} = (x + y)(x^{2} – xy + y^{2})

= [(2a)^{3} – 3^{3}][(2a)^{3} + 3^{3}]

= (2a)^{6} - 3^{6}

= 64a^{6} – 729

**iv.** (x – y)(x^{2} + xy + y^{2}) + (y – z)(y^{2} + yz + z^{2}) + (z – x)(z^{2} + zx + x^{2})

Using a^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})

= x^{3} – y^{3} + y^{3} – z^{3} + z^{3} – x^{3}

= 0

**v.** (x + 1)(x^{2} - x + 1) + (2x – 1)(4x^{2} + 2x + 1) – (x – 1)(x^{2} + x + 1)

= (x + 1)(x^{2} - x + 1) + (2x – 1)((2x)^{2} + 2x + 1) – (x – 1)(x^{2} + x + 1)

Using x^{3} – y^{3} = (x – y)(x^{2} + xy + y^{2})

x^{3} + y^{3} = (x + y)(x^{2} – xy + y^{2})

= x^{3} + 1 + (2x)^{3} – 1 - (x^{3} – 1)

= x^{3} + 1 + 8x^{3} – 1 – x^{3} + 1

= 8x^{3} + 1

Rate this question :

Let us write in the blank box:

West Bengal - Mathematics

Let’s resolve into factors the following algebraic expressions:

i.

ii.

iii.

iv.

v.

vi.

vii.

viii.

ix.

x.

xi.

xii.

xiii.

xiv.

xv.

xvi.

xvii.

West Bengal - Mathematics

Let’s find the value of by calculation if

West Bengal - MathematicsLet’s find the value of by calculation if

or,

or,

or, [by transposition]

[With the help of the identity No. VI]

West Bengal - Mathematics

Let’s find the value of by calculation if

West Bengal - Mathematics