Simplify. (i) (x^2 − 5) (x + 5) + 25 (ii) (a^2 + 5) (b^3 + 3) + 5 (iii) (t + s^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)
Answers
Answer with Step-by-step explanation:
Solution:
i) (x² - 5)(x + 5) + 25
= x²(x + 5) - 5(x + 5) + 25
= x³+ 5x² - 5x - 25 + 25
= x³ + 5x² - 5x
ii) (a² + 5)(b³ + 3) + 5
a²(b³ + 3) + 5(b³ + 3)
a²b³ + 3a² + 5b³ + 15 + 5
= a²b³ + 5b³ + 3a² + 20
iii) (t + s²)(t² - s)
t(t² - s) + s²(t² - s)
t³- ts + s²t² - s³
iv) (a + b)(c - d) + (a - b)(c + d) + 2(ac + bd)
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)
= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd
= ac + ac + 2ac - ad + ad + bc - bc - bd - bd + 2bd
= 4ac
v) (x + y) (2x + y) + (x + 2y) (x − y)
= x(2x + y)+y(2x + y) + x(x-y)+2y(x-y)
=2x² + xy + 2xy + y² + x² - xy + 2xy - 2y²
= 2x² + x² + xy - xy + 2xy + 2xy + y² - 2y²
= 3x² + 4xy - y²
vi) (x + y) (x² − xy + y²)
x(x² − xy + y²) +y(x² -xy+y²)
= x³- x²y + xy² + x²y – xy² +y³
= x³ - x²y + x²y + xy² - xy² + y³
= x³ + y³
vi) (1.5x − 4y) (1.5x + 4y + 3) − 4.5x + 12y
= 1.5x(1.5x + 4y + 3) -4y(1.5x + 4y + 3) - 4.5x + 12y
= .25x² + 6xy + 4.5x - 6xy - 16y² - 12y - 4.5x + 12y
= 2.25x² + 6xy - 6xy + 4.5x - 4.5x - 12y + 12y - 16y²
= 2.25x² - 16y²
vii) (a + b + c) (a + b − c)
= a(a + b − c)+b(a + b − c)+c(a + b − c)
= a² + ab - ac + ab + b² - bc + ac + bc - c²
= a² + ab + ab - ac + ac + b² - c² + bc - bc
= a² + 2ab + b² - c²
HOPE THIS ANSWER WILL HELP YOU....
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