Question

factories by using middle term spitting x square +10x+21 (b) a square +8a+16 (c) p square -10p +25 (d) y square -7y+12​

Answer 1

`\bold{\huge{\underline{ Solution }}}`

• Quadratic equation is defined as the equation having highest power of degree as 2 .

• The general form of quadratic equation is ax² + bx + c

• Generally, we solve quadratic equations by factorization method but it not applicable for two quadratic equations.

• Factorization method is also applicable for linear, cubic etc.

• When we have two different types of quadratic equations then we use substitution method, elimination method and cross multiplication method.

• Factorization method is also known as middle term splitting method.

Let's come to the solution now,

Solution 1 :-

Here, we have equation

• 
  `\sf{ x^(2) + 10x + 21 }`

By using factorisation method

• 
  `\sf{ x^(2) + 3x + 7x + 21 }`

[ Here, we have taken 3 and 7 because "7 + 3 = 10 " and " 7 × 3 = 21 ]

`\sf{ x( x + 3) + 7( x + 3 )}`

`\sf{ ( x + 3 ) ( x + 7) }`

Hence, The required answer is

(x + 3)(x + 7) .

Solution 2 :-

Here ,we have equation

• 
  `\sf{ a^(2) + 8a + 16 }`

By using factorisation method,

• 
  `\sf{ a^(2) + 4a + 4a + 16 }`

[ Here, we have taken 4 and 4 because "4 + 4 = 8 " and " 4 × 4 = 16 ]

`\sf{ a( a + 4) + 4( a + 4) }`

`\sf{ ( a + 4) ( a + 4) }`

Hence, The required answer is

( a + 4)( a + 4) .

Solution 3 :-

Here, we have equation ,

• 
  `\sf{ p^(2) - 10p + 25 }`

By using factorisation method,

• 
  `\sf{ p^(2) - 5p - 5p + 25 }`

[ Here, we have taken - 5 and -5 because "-5 + (-5) = -5 - 5 = - 10 " and " -5 × -5 = 25]

`\sf{ p( p - 5) - 5(p - 5) }`

`\sf{ ( p - 5) (p - 5) }`

Hence, The required answer is

(p - 5)( p - 5) .

Solution 4 :-

Here, we have equation

• 
  `\sf{ y^(2) - 7y + 12 }`

By using factorisation method ,

• 
  `\sf{ y^(2) - 4y - 3y + 12 }`

[ Here, we have taken -4 and -3 because "- 4 + (- 3) = -4 - 3 = - 7 " and " -4 × -3 = 12]

`\sf{ y( y - 4 ) - 3 ( y - 4 ) }`

`\sf{ ( y - 3) ( y - 4) }`

Hence, The required answer is

(y - 3)( y - 4) .