Find the following products: ​ (i) (3x^2-4xy)(3x^2-3xy) (ii) ​(x+1/5)(x+5) (iii) (z+3/4)(z+4/3)

Question

Find the following products:

(i) (3x²-4xy)(3x²-3xy)

(ii) \((x+\frac{1}{5})(x+5)\)

(iii) \((z+\frac{3}{4})(z+\frac{4}{3})\)

(iv) (x²+4)(x²+9)

(v) (y²+12)(y²+6)

(vi) \((y^2+\frac{5}{7})(y^2-\frac{14}{5})\)

(vii) \((p^2+16)(p^2-\frac{1}{4})\)

Answer 1

(i) (3x²-4xy)(3x²-3xy)

3x² (3x² – 3xy) – 4xy (3x² – 3xy)

= 9x⁴ – 9x³y – 12x³y + 12x²y²

= 9x⁴ – 21x³y + 12x²y²

(ii) \((x+\frac{1}{5})(x+5)\)

x (x + \(\frac{1}{5}\)) + 5 (x + \(\frac{1}{5}\))

= x² + \(\frac{x}{5}\) + 5x + 1

= x² + \(\frac{26}{5}\)x + 1

(iii) \((z+\frac{3}{4})(z+\frac{4}{3})\)

z (z + \(\frac{4}{3}\)) + \(\frac{3}{4}\)(z + \(\frac{4}{3}\))

= z² + \(\frac{4}{3}\)z + \(\frac{3}{4}\)z + \(\frac{12}{12}\)

= z² + \(\frac{4}{3}\)z + \(\frac{3}{4}\)z + 1

= z² + \(\frac{25}{12}\)z + 1

(iv) (x²+4)(x²+9)

x² (x² + 9) + 4 (x² + 9)

= x⁴ + 9x² + 4x² + 36

= x⁴ + 13x² + 36

(v) (y²+12)(y²+6)

y² (y² + 6) + 12 (y² + 6)

= y⁴ + 6y² + 12y² + 72

= y⁴ + 18y² + 72

(vi) \((y^2+\frac{5}{7})(y^2-\frac{14}{5})\)

y² (y² - \(\frac{14}{5}\)) + \(\frac{5}{7}\)(y² - \(\frac{14}{5}\))

= y⁴ - \(\frac{14}{5}\)y² + \(\frac{5}{7}\)y² – 2

= y⁴ - \(\frac{73}{35}\)y² - 2

(vii) \((p^2+16)(p^2-\frac{1}{4})\)

p² (p² - \(\frac{1}{4}\)) + 16 (p² - \(\frac{1}{4}\))

= p⁴ – \(\frac{1}{4}\)p² + 16p² – 4

= p⁴ - \(\frac{63}{4}\)p² - 4