Question

Simplify
(i) $(x^2-5)(x+5)+25$
(ii) $(a^2+5)(b^3+3)+5$
(iii) $(t+8^2)(t^2-s)$
(iv) $(a+b)(c-d)+(a-b)(c+d)+2(ac+bd)$
(v) $(x+y)(2x+y)+(x+2y)(x-y)$
(vi) $(x+y)(x^2-xy+y^2)$
(vii) $(1.5x-4y)(1.5x+4y+3)-4.5x+12y$
(viii) $(a+b+c)(a+b-c)$

Answer 1

(i) $x^2(x+5)-5(x+5)+25$
$=x^3+5x^2-5x-25+25$

$=x^3+5x^2-5x$

(ii) $a^2{b}^3+3a^2+5b^3+15+5$
$=a^2{b}^3+3a^2+5b^3+20$

(iii) $t(t^2-s)+s^2(t^2-s)$
$=t^3-st+s^2{t}^2-s^3$

(iv) $a(c-d)+b(c-d)+a(c+d)-b(c+d)+2(ac+bd)$
$=ac-ad+bc-bd+ac+ad-bc-bd+2ac+2bd$
$=4ac$

(v) $2x^2+xy+2xy+y^2+x^2-xy+2xy-2y^2$
$=2x^2+x^2+y^2-2y^2+xy+2xy-xy+2xy$
$=3x^2+4xy-y^2$

(vi) $x^3-x^{2}y+x{y}^2+x^{2}y-x{y}^2+y^3$
$=x^3+y^3+(x{y}^2-x{y}^2)+(x^{2}y-x^{2}y)$
$=x^3+y^3$

(vii) $2.25x^2+6xy+4.5x-6xy-16y^2-12y-4.5x+12y$
$=2.25x^2-16y^2$

(viii) $a(a+b+c)+b(a+b-c)+c(a+b-c)$
$=a^2+ab-ac+ab+b^2-bc+ac+bc-c^2$
$=a^2+b^2-c^2+(ab+ab)+(bc-bc)+(ca-ca)$
$=a^2+b^2-c^2+2ab$