Q. 5 D5.0( 1 Vote )

# Find the product of the following :

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

Answer :

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

⇒ (a × a^{2} + a × 2ab + a × b^{2}) + (b × a^{2} + b × 2ab + b× b^{2})

⇒ (a^{2 + 1} + 2a^{1 + 1}b + ab^{2}) + (ba^{2} + 2ab^{1 + 1} + b^{2 + 1})

(∵ a^{n + m} = a^{n} × a^{m})

⇒ (a^{3} + 2a^{2}b + ab^{2}) + (ba^{2} + 2ab^{2} + b^{3})

⇒ a^{3} + 2a^{2}b + a^{2}b + ab^{2} + 2ab^{2} + b^{3}

⇒ a^{3} + (2 + 1)a^{2}b + (1 + 2)ab^{2} + b^{3}

⇒ a^{3} + 3a^{2}b + 3ab^{2} + b^{3}

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Find the product of the following pairs of monomials:

i. 3, 7x

ii. – 7x, 3y

iii. – 3a, 5ab

iv. 5a^{2}, – 4a

v.

vi. Xy^{2}, x^{2}y

vii. x^{3}y^{5}, xy^{2}

viii. abc, abc

ix. xyz. x^{2}yz

x. a^{2}b^{2}c^{3}, abc^{2}

Find the product of the following :

(x + y + z) (x + y – z)

Tamilnadu - Math Term-2Find the product of the following :

(2x + 3y) (x^{2} – xy + y^{2})

Find the product of the following :

(a + b) (2a^{2} – 5ab + 3b^{2})

Find the product :

(i) (a^{3}) × (2a^{5}) × (4a^{15})

(ii) (5 – 2x) (4 + x)

(iii) (x + 3y) (3x – y)

(iv) (3x + 2) (4x – 3)

(v)

Tamilnadu - Math Term-2Find out the product :

(i) 2a, 3a^{2}, 5a^{4}

(ii) 2x, 4y, 9z

(iii) ab, bc, ca

(iv) m, 4m, 3m^{2}, - 6m^{3}

(v) xyz, y^{2}z, yx^{2}

(vi) lm^{2}, mn^{2}, ln^{2}

(vii) -2p, -3q, -5p^{2}

Complete the following table of products:

Tamilnadu - Math Term-2

Find the product of the following :

(m – n) (m^{2} + mn + n^{2})

Find the product of the following :

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