Q. 5 B5.0( 1 Vote )

# Find the product of the following :

(2x + 3y) (x^{2} – xy + y^{2})

Answer :

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

⇒ (2x × x^{2} – 2x × xy + 2x × y^{2}) + (3y × x^{2} -3y × xy + 3y× y^{2})

⇒ (2x^{2 + 1} – 2x^{1 + 1}y + 2xy^{2}) + (3yx^{2} -3xy^{1 + 1} + 3y^{2 + 1})

(∵ a^{n + m} = a^{n} × a^{m})

⇒ (2x^{2 + 1} – 2x^{1 + 1}y + 2xy^{2}) + (3yx^{2} -3xy^{1 + 1} + 3y^{2 + 1})

⇒ (2x^{3} – 2x^{2}y + 2xy^{2}) + (3yx^{2} -3xy^{2} + 3y^{3})

⇒ 2x^{3} – 2x^{2}y + 3x^{2}y + 2xy^{2} -3xy^{2} + 3y^{3}

⇒ 2x^{3} (- 2 + 3)x^{2}y + (2-3)xy^{2} + 3y^{3}

⇒ 2x^{3} + x^{2}y - xy^{2} + 3y^{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})