Question

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

Answer 1

We use identities

$(x+a)(x+b)=x^2+(a+b)x+ab$ and $x^2-y^2=(x+y)(x-y)$

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

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

$=x^2+14x+40$

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

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

$=x^2-2x-80$

(iii) $(3x+4)(3x+5)$
$=(3x{)}^2+(4-5)3x+(4\left)\right(-5)$

$=9x^2-3x-20$

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

$=(y^2{)}^2-{\left(\frac{3}{2}\right)}^2$

$=y^4-\frac{9}{4}$

(v) $(3-2x)(3+2x)$

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