Question
Complete the following table.
✓
Answer
(i) First expression : $9 x y$
Second expression : $-4 x(x+y)$
Product : $9 x y \times[-4 x(x+y)]$
$=-36 x^2 y(x+y)$
$=-36 x^2 y \times x+\left(-36 x^2 y \times y\right)$
$=-36 x^3 y-36 x^2 y^2$
(ii) First expression: pq
Second expression : $-9 p^2-7 q^2$
Product: $p q\left(-9 p^2-7 q^2\right)$
$=-p q \times 9 p^2-7 q^2 \times p q$
$=-9 p^3 q-7 p q^3$
(iii) First expression : $a^2+b^2+c^2$
Second expression : $-5 a b c$
Product: $-5 a b c \times\left(a^2+b^2+c^2\right)$
$=-5 a b c \times a^2-5 a b c \times b^2-5 a b c \times c^2$
$=-5 a^3 b c-5 a b^3 c-5 a b c^3$
(iv) First expression : $9 x+5 y-2$
Second expression : $x^2 y^2$
Product : $x^2 y^2 \times(9 x+5 y-2)$
$=x^2 y^2 \times 9 x+x^2 y^2 \times 5 y-x^2 y^2 \times 2$
$=9 x^3 y^2+5 x^2 y^3-2 x^2 y^2$
(v) First expression : $-\frac{5}{3} p^2 q^2$
Second expression : $6 p q-9 q^2$
Product $:-\frac{5}{3} p^2 q^2 \times\left(6 p q-9 q^2\right)$
$=-\frac{5}{3} p^2 q^2 \times 6 p q+\frac{5}{3} p^2 q^2 \times 9 q^2$
$=-10 p^3 q^3+15 p^2 q^4$
Second expression : $-4 x(x+y)$
Product : $9 x y \times[-4 x(x+y)]$
$=-36 x^2 y(x+y)$
$=-36 x^2 y \times x+\left(-36 x^2 y \times y\right)$
$=-36 x^3 y-36 x^2 y^2$
(ii) First expression: pq
Second expression : $-9 p^2-7 q^2$
Product: $p q\left(-9 p^2-7 q^2\right)$
$=-p q \times 9 p^2-7 q^2 \times p q$
$=-9 p^3 q-7 p q^3$
(iii) First expression : $a^2+b^2+c^2$
Second expression : $-5 a b c$
Product: $-5 a b c \times\left(a^2+b^2+c^2\right)$
$=-5 a b c \times a^2-5 a b c \times b^2-5 a b c \times c^2$
$=-5 a^3 b c-5 a b^3 c-5 a b c^3$
(iv) First expression : $9 x+5 y-2$
Second expression : $x^2 y^2$
Product : $x^2 y^2 \times(9 x+5 y-2)$
$=x^2 y^2 \times 9 x+x^2 y^2 \times 5 y-x^2 y^2 \times 2$
$=9 x^3 y^2+5 x^2 y^3-2 x^2 y^2$
(v) First expression : $-\frac{5}{3} p^2 q^2$
Second expression : $6 p q-9 q^2$
Product $:-\frac{5}{3} p^2 q^2 \times\left(6 p q-9 q^2\right)$
$=-\frac{5}{3} p^2 q^2 \times 6 p q+\frac{5}{3} p^2 q^2 \times 9 q^2$
$=-10 p^3 q^3+15 p^2 q^4$
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