Question

Question 1
Use suitable identities to find the following products:
(i) (x + 4) (x + 10)
(ii) (x+8) (x-10)
(iii) (3x + 4) (3x-5)
(iv) $(y^2+\frac{3}{2})(y^2-\frac{3}{2})$
(c) (3-2x) (3+2x)

Answer 1

(i) Using identity (x + a) (x + b) = $x^2+(a+b)x+ab,(x+4)(x+10)=x^2+(4+10)x+4\times 10=x^2+14x+40$

(ii) Using the same identity as in (i) above,
(x + 8) (x - 10) = $x^2+(8-10)x+8(-10)=x^2-2x-80$

(iii) Using the same identity,
$(3x+4)(3x-5)=3x\times 3x+(-1)\left(3x\right)-20=9x^2-3x-20$

(iv) Using $(x+y)(x-y)=x^2-y^2(y^2+\frac{3}{2})(y^2-\frac{3}{2})=(y^2{)}^2-{\left(\frac{3}{2}\right)}^2=y^4-\frac{9}{4}$
(v) Using the same identity as in (iv),
$(3-2x)(3+2x)=3^2-(2x{)}^2=9-4x^2$