Simplify -x-2-x-4- - -x-1-x-1-6x - 9x-2 - 6x - 9-6x - 9 nbsp-6x - 7

The correct option is A 6x + 9We know, (x+a)(x+b) = x^2 + (a+b)x + ab ⇒ (x+2)(x+4) = x^2 + (2+4)x + (2)(4) = x^2 + 6x + 8 We also know, nbsp; (x+a)(x a) = ...

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Byju's Answer

Standard IX

Mathematics

Identity (x+a)(x+b)

Simplify (x+2...

Question

Simplify $(x + 2) (x + 4) - (x + 1) (x - 1)$ .

6 x + 7

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6 x + 9

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x^{2} + 6 x + 9

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- 6 x + 9

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Solution

The correct option is B $6 x + 9$
We know,
$(x + a) (x + b) = x^{2} + (a + b) x + a b$

$\Rightarrow (x + 2) (x + 4) = x^{2} + (2 + 4) x + (2) (4) = x^{2} + 6 x + 8$

We also know,
$(x + a) (x - a) = x^{2} - a^{2}$
$\Rightarrow (x + 1) (x - 1) = x^{2} - 1^{2} = x^{2} - 1$

$\Rightarrow (x + 2) (x + 4) - (x + 1) (x - 1)$
$= x^{2} + 6 x + 8 - (x^{2} - 1$ )
$= x^{2} + 6 x + 8 - x^{2} + 1$
$= 6 x + 9$

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Similar questions

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(v)

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Q. The factors of x³ − 7x + 6 are

(a) x (x − 6) (x − 1)

(b) (x² − 6) (x − 1)

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(d) (x − 1) (x + 3) (x − 2)

Q. Simplify:

x^{2} + 6 x + 9 - 4 y^{2}

Q. Simplify

x^{2} + 6 x + 9

using suitable identity.

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Simplify (x+2)(x+4)−(x+1)(x−1).

The correct option is B 6x+9We know, (x+a)(x+b)=x2+(a+b)x+ab ⇒(x+2)(x+4)=x2+(2+4)x+(2)(4)=x2+6x+8 We also know, (x+a)(x−a)=x2−a2 ⇒(x+1)(x−1)=x2−12=x2−1 ⇒(x+2)(x+4)−(x+1)(x−1) =x2+6x+8−(x2−1) =x2+6x+8−x2+1 =6x+9

Simplify $(x + 2) (x + 4) - (x + 1) (x - 1)$ .