Question

Use the identity $(x+a)(x+b)=x^2+(a+b)x+ab$ to find following products.
(i) $(x+3)(x+7)$
(ii) $(4x+5)(4x+1)$
(iii) $(4x-5)(4x-1)$
(iv) $(4x+5)(4x-1)$
(v) $(2x+5y)(2x+3y)$
(vi) $(2a^2+9)(2a^2+5)$
(vii) $(xyz-4)(xyz-2)$

Answer 1

(i) $(x+3)(x+7)$

$=x^3+(3+7)x+\left(3\right)\left(7\right)$

$=x^2+10x+21$

(ii) $(4x{)}^2+(5+1)4x+(5\left)\right(1)$
$=16x^2+24x+5$

(iii) $(4x-5)(4x-1)$

$=(4x{)}^2+[(-5)+(-1)]4x+(-5\left)\right(-1)$
$=16x^2-24x+5$

(iv) $(4x{)}^2+[\left(5\right)+(-1)]4x+(5\left)\right(-1)$
$16x^2+16x-5$

(v) $(2x{)}^2+(5y+3y\left)\right(2x)+(5y\left)\right(3y)$
$=4x^2+16xy+15y^2$

(vi) $(2a^2{)}^2+(9+5\left)\right(2a^2)+(9\left)\right(5)$
$=4a^2+28a^2+45$

(vii) $(xyz{)}^2+[(-4)+(-2)\left]\right(xyz)+(-4\left)\right(-2)$
$=x^2{y}^2{z}^2-6xyz+8$