Question

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

Answer 1

(i) $(x+4)(x+10)$

Here, we can use an identity: $(x+a)(x+b)$ = $x^2$$+(a+b)x+ab$.. (1)

In this problem, we have $a=4andb=10$.

So, putting values in (1), we get

$(x+4)(x+10)$=$x^2$$+(4+10)x+\left(4\right)\left(10\right)$= $x^2$$+14x+40$

(ii) $(x+8)(x-10)$

$=(x+8)[x+(-10\left)\right]$

Here, we can use an identity: $(x+a)(x+b)=$ $x^2$$+(a+b)x+ab$..(2)

In this problem, we have $a=8\text{and}b=-10$

So, putting values in (2), we get

$(x+8)(x-10)=$ $x^2$$+(8-10)x+\left(8\right)(-10)=$$x^2$$-2x-80$

(iii) ($y^2$+$\frac{3}{2}$)($y^2$−$\frac{3}{2}$)

Here, we can use an identity: $(a+b)(a-b)$=$a^2$−$b^2$..... (3)

We have $a=$$y^2$ and $b=$ $\frac{3}{2}$

Putting values in (3), we get

($y^2$+$\frac{3}{2}$)($y^2$−$\frac{3}{2}$)=${\left(y^2\right)}^2$−${\left(\frac{3}{2}\right)}^2$= $y^4$−$\frac{9}{4}$