Question

Please solve all questions Q.5

Answer 1

a. a² + 2ab - 24b²

= a² - 4ab + 6ab - 24b²

= a(a - 4b) + 6b(a - 4b)

= (a + 6b)(a - 4b)

b. t² - 2pt - 35p²

= t² - 7pt + 5pt - 35p²

= t(t - 7p) + 5p(t - 7p)

= (t + 5p)(t - 7p)

c. 35x² - 11xy - 6y²

(Multiply the coefficient of x² in 6y²)

= x² - 11xy - 210y²

= x² + 10xy - 21xy - 210y²

= x(x + 10y) - 21y(x + 10y)

= (x - 21y)(x + 10y)

Now multiply 35 to x term

= (35x - 21y)(35x + 10y)

= 7(5x - 3y)5(7x + 2y)

Ignoring constant terms,

= (5x - 3y)(7x + 2y)

d. 4p² + 12pq - 27q²

(Multiply the coefficient of p² in 27q²)

= p² + 12pq - 108q²

= p² + 18pq - 6pq - 108q²

= p(p + 18q) - 6q(p + 18q)

= (p - 6q)(p + 18q)

Now multiply 4 to x term,

= (4p-6q)(4p + 18q)

= 2(2p - 3q)2(2p + 9q)

Ignoring the constant terms,

= (2p - 3q)(2p + 9q)