Question

Factorize the following expressions and write them in the product form
1. 201a³b²
2. 91xyt²
3. 24a² b²
Also, explaining how to factorize a binomial would help me a lot :)

Answer 1

To factorise:

• 201a³b²
• 91xyt²
• 24a² b²

Solution:

1. 201a³b²

$\implies \sf{201a^3b^2}$

Here, $\sf{201 = 3 \times 67}$

${ \therefore \; \boxed{\orange{\sf{ 201a^3b^2 = 3 \times 67 \times a \times a \times a \times b \times b } }}}$

   

Solution:

2. 91xyt²

$\implies \sf{91xyt^2}$

Here, $\sf{ 91 = 7 \times 13 }$

${ \therefore \; \boxed{\orange{\sf{ 91xyt^2 = 7 \times 13 \times x \times y \times t \times } }}}$

   

Solution:

3. 24a² b²

$\implies \sf{24a^2b^2}$

Here, $\sf{ 24 = 2 \times 12 }$

${ \therefore \; \boxed{\orange{\sf{ 24a^2 b^2 = 2 \times 12 \times a \times a \times b \times b } }}}$

   

Factorising a binomial:

We can factorize a binomial by identifying the factors common to both terms & writing them outside the brackets in product form.

This is how we factorize:

Example: 4xy + 8xy²

⇒ 4 (xy + 2xy²)

⇒ 4x (y + 2y²)

⇒ 4xy (1 + 2y)

   

Here, 4, x & y are factors of every term in the binomial 4xy + 8xy².

Also, (a + b)(a - b) = a² - b² is a formula we have already learnt.

Hence, we get the factors:

a² - b² = (a + b)(a - b)

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* ⁺◦﹆◞˚ ꒰ More to know ꒱    

⬩ Related Algebraic Identities :    

→ (a + b)² = a² + 2ab + b²

→ (a - b)² = a² - 2ab + b²

→ (a + b) (a - b) = a² - b²

→ (a + b)³ = a³ + 3a²b + 3ab² + b³

→ (a - b)³ = a³ - 3a²b + 3ab² + b³

→ (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

→ (x + a) (x + b) = x² + (a + b)x + ab

→ a³ + b³ = (a + b) (a² - ab + b²)

→ a³ - b³ = (a - b) (a² + ab + b²)

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Apologies for the mistakes.

Answer 2

To factorise:

201a³b²

91xyt²

24a² b²

Solution:

1. 201a³b²

$\implies \sf{201a^3b^2}$

Here, $\sf{201 = 3 \times 67}$

${ \therefore \; \boxed{\purple{\sf{ 201a^3b^2 = 3 \times 67 \times a \times a \times a \times b \times b } }}}$

Solution:

2. 91xyt²

$\implies \sf{91xyt^2}$

Here, $\sf{ 91 = 7 \times 13 }$

${ \therefore \; \boxed{\purple{\sf { 91xyt^2 = 7 \times 13 \times x \times y \times t \times } }}}$

Solution:

3. 24a² b²

$\implies \sf{24a^2b^2}$

Here,$\sf{ 24 = 2 \times 12 }$

${ \therefore \; \boxed{\purple{\sf{ 24a^2 b^2 = 2 \times 12 \times a \times a \times b \times b } }}}$