Q. 84.1( 9 Votes )

# Let us factorise the following algebraic expressions:

3a (3a + 2c) – 4b (b + c)

Answer :

Given, 3a(3a + 2c) – 4b(b + c)

⇒ 9a^{2} + 6ac – 4b^{2} – 4bc

⇒ (3a)^{2} + 2(3)(ac) – (2b)^{2} – 4bc + c^{2} – c^{2}

⇒ (3a)^{2} + 2(3)(ac) + c^{2} – ((2b)^{2} + 2(2b)(c) + c^{2})

⇒ (3a + c)^{2} – (2b + c)^{2}

[Since, from the identity III we know that, (x^{2} – y^{2}) = (x – y)(x + y)]

⇒ (3a + c – 2b – c)(3a + c + 2b + c)

⇒ (3a – 2b)(3a + 2b + 2c)

Rate this question :

Let us calculate and write, which of the following polynomials will have a factor (x + 1)?

x^{4} + x^{3} – x^{2} + 4x + 5

If (x + 1) and (x + 2) are two factors of the polynomial x^{3} + 3x^{2} + 2ax + b, then let us calculate and write the values of a and b.

Let us calculate and write, which of the following polynomials will have a factor (x + 1)?

x^{4} + x^{2} + x + 1

By using Factor Theorem, let us write whether g(x) is a factor of the following polynomials f(x).

f(x) = 2x^{3} + 7x^{2} – 24x – 45 and g(x) = x – 3

By using Factor Theorem, let us write whether g(x) is a factor of the following polynomials f(x).

f(x) = 2x^{3} + 9x^{2} – 11x – 30 and g(x) = x + 5

Let us factorise the following algebraic expressions:

1 + 8x^{3} + 18xy – 27y^{3}

Let us factorise the following algebraic expressions:

3a (3a + 2c) – 4b (b + c)

West Bengal MathematicsBy using Factor Theorem, let us write whether g(x) is a factor of the following polynomials f(x).

f(x) = 3x^{3} + x^{2} – 20x + 12 and g(x) = 3x – 2