Use suitable identities to find the following products:
(i) $(x + 4) (x + 10)$
(ii) $(x + 8) (x - 10)$
(iii) $(3 x + 4) (3 x - 5)$
(iv) $(y^{2} + \frac{3}{2}) (y^{2} - \frac{3}{2})$
(v) $(3 - 2 x) (3 + 2 x)$

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Solution

We use identities
$(x + a) (x + b) = x^{2} + (a + b) x + a b$ and $x^{2} - y^{2} = (x + y) (x - y)$

(i) $(x + 4) (x + 10)$
$= x^{2} + (4 + 10) x + (4) (10)$
$= x^{2} + 14 x + 40$

(ii) $(x + 8) (x - 10)$
$= x^{2} + (8 - 10) + (8) (- 10)$
$= x^{2} - 2 x - 80$

(iii) $(3 x + 4) (3 x + 5)$
$= (3 x)^{2} + (4 - 5) 3 x + (4) (- 5)$
$= 9 x^{2} - 3 x - 20$

(iv) $(y^{2} + \frac{3}{2}) (y^{2} - \frac{3}{2})$
$= (y^{2})^{2} - {(\frac{3}{2})}^{2}$
$= y^{4} - \frac{9}{4}$

(v) $(3 - 2 x) (3 + 2 x)$
$= (3)^{2} - (2 x)^{2} = 9 - 4 x^{2}$

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Similar questions

Q. Question 1
Use suitable identities to find the following products:
(i) (x + 4) (x + 10)
(ii) (x+8) (x-10)
(iii) (3x + 4) (3x-5)
(iv)

(y^{2} + \frac{3}{2}) (y^{2} - \frac{3}{2})

Use suitable identities to find the following products:
(i) $(x + 4) (x + 10)$
(ii) $(x + 8) (x - 1)$
(iii) ( $y^{2}$ + $\frac{3}{2}$ )( $y^{2}$ − $\frac{3}{2}$ )

Question 1
Use suitable identities to find the following products:
(i) (x + 4) (x + 10)
(ii) (x+8) (x-10)
(iii) (3x + 4) (3x-5)
(iv) $(y^{2} + \frac{3}{2}) (y^{2} - \frac{3}{2})$
(c) (3-2x) (3+2x)

Use suitable identities to find the following product: ( $y^{2}$ + $\frac{3}{2}$ )( $y^{2}$ – $\frac{3}{2}$ )

Q. Use suitable identities to find the following products:

(y^{2} + \frac{3}{2}) (y^{2} - \frac{3}{2})

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Use suitable identities to find the following products:(i) (x+4)(x+10)(ii) (x+8)(x−10)(iii) (3x+4)(3x−5)(iv) (y2+32)(y2−32)(v) (3−2x)(3+2x)

Use suitable identities to find the following products:
(i) $(x + 4) (x + 10)$
(ii) $(x + 8) (x - 10)$
(iii) $(3 x + 4) (3 x - 5)$
(iv) $(y^{2} + \frac{3}{2}) (y^{2} - \frac{3}{2})$
(v) $(3 - 2 x) (3 + 2 x)$