Advertisements
Advertisements
Question
Simplify : (2.5p − 1.5q)2 − (1.5p − 2.5q)2
Advertisements
Solution
To simplify, we will proceed as follows:
\[\left( 2 . 5p - 1 . 5q \right)^2 - \left( 1 . 5p - 2 . 5q \right)^2 \]
\[ = \left( 2 . 5p \right)^2 + \left( 1 . 5q \right)^2 - 2\left( 2 . 5p \right)\left( 1 . 5q \right) - \left[ \left( 1 . 5p \right)^2 + \left( 2 . 5q \right)^2 - 2\left( 1 . 5p \right)\left( 2 . 5q \right) \right] \]
\[ = \left( 2 . 5p \right)^2 + \left( 1 . 5q \right)^2 - 2\left( 2 . 5p \right)\left( 1 . 5q \right) - \left( 1 . 5p \right)^2 - \left( 2 . 5q \right)^2 + 2\left( 1 . 5p \right)\left( 2 . 5q \right)\]
\[ = \left( 2 . 5p \right)^2 - \left( 1 . 5p \right)^2 + \left( 1 . 5q \right)^2 - \left( 2 . 5q \right)^2 \]
\[ = \left[ \left( 2 . 5p + 1 . 5p \right)\left( 2 . 5p - 1 . 5p \right) \right] + \left[ \left( 1 . 5q + 2 . 5 \right)\left( 1 . 5q - 2 . 5q \right) \right] \left[ \because \left( a + b \right)\left( a - b \right) = a^2 - b^2 \right] \]
\[ = 4p \times p + 4q \times \left( - q \right)\]
\[ = 4 p^2 - 4 q^2 \]
\[ = 4\left( p^2 - 4 q^2 \right) \]
APPEARS IN
RELATED QUESTIONS
Find each of the following product:
(7ab) × (−5ab2c) × (6abc2)
Find each of the following product:
(−4x2) × (−6xy2) × (−3yz2)
Find the value of (5x6) × (−1.5x2y3) × (−12xy2) when x = 1, y = 0.5.
Find the following product: \[\frac{7}{5} x^2 y\left( \frac{3}{5}x y^2 + \frac{2}{5}x \right)\]
Simplify: a(b − c) + b(c − a) + c(a − b)
Simplify: a2(2a − 1) + 3a + a3 − 8
Multiply:
(x2 + y2) by (3a + 2b)
Simplify:
(x3 − 2x2 + 5x − 7)(2x − 3)
Simplify:
(3x − 2)(2x − 3) + (5x − 3)(x + 1)
Multiply:
16xy × 18xy
