What is the value of \( p^{2} q-q^{2} p \) if \( p=3 \) and \( q=-1 \) ? [WAEC] (4) Evaluate \( x^{2}+3 x+2 \) when \( x= \) a 1, b \( 0, \quad \) c \( -1, d-2 \) (f) Evaluate \( p^{2}-2 p-3 \) when \( p= \) a \( 4, \quad \) b \( 3, \quad \) c 1, d 0, e \( -1, f-2 \) (6) Evaluate \( 3 a^{2}-2 a+5 \) if \( a= \) a \( 2, \quad \) b \( 0, \quad \) c \( -2, d-4 \) Evaluate \( z^{3}-z \) if \( z= \) a \( 2, \quad \) b \( 1, \quad \) c \( 0, \quad d-1 \), e -2 . Evaluate \( a b \sqrt{c^{2}+b^{2}} \), given that \( a=2 \), \( b=-3, c=4 \). [WAEC] If \( a=-3, b=2, c=1 \) and \( d=-4 \), find the values of a \( 5 b-a d \), b \( (b a)^{2}-b d^{2} \), \( c\left(\frac{c-a}{b-d}\right)^{2} \)

To find the value of \( p^{2} q - q^{2} p \) when \( p=3 \) and \( q=-1 \), first calculate \( p^{2} q = 3^{2} \cdot (-1) = 9 \cdot (-1) = -9 \) and \( -q^{2} p = -(-1)^{2} \cdot 3 = -1 \cdot 3 = -3 \). Therefore, \( p^{2} q - q^{2} p = -9 - (-3) = -9 + 3 = -6 \). Now, for the evaluation of \( x^{2}+3x+2 \): - a: \( x = 1 \): \( 1^{2} + 3(1) + 2 = 1 + 3 + 2 = 6 \). - b: \( x = 0 \): \( 0^{2} + 3(0) + 2 = 0 + 0 + 2 = 2 \). - c: \( x = -1 \): \( (-1)^{2} + 3(-1) + 2 = 1 - 3 + 2 = 0 \). - d: \( x = -2 \): \( (-2)^{2} + 3(-2) + 2 = 4 - 6 + 2 = 0 \). Enjoy the math journey! Each equation has a character of its own, just like embarking on small adventures where numbers become friends and their interactions create delightful outcomes.