Simplify:

$(i) (x - y) (x + y) (x^{2} + y^{2}) (x^{4} + y^{4})$ $(i i) (2 x - 1) (2 x + 1) (4 x^{2} + 1) (16 x^{4} + 1)$

$(i i i) (7 m - 8 n)^{2} + (7 m + 8 n)^{2}$ $(i v) (2.5 p - 1.5 q)^{2} - (1.5 p - 2.5 q)^{2}$

$(v) (m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}$

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Solution

$(i) (x - y) (x + y) (x^{2} + y^{2}) (x^{4} + y^{4}) = (x^{2} - y^{2}) (x^{2} + y^{2}) (x^{4} + y^{4}) = [(x^{2})^{2} - (y^{2})^{2}] (x^{4} + y^{4}) = (x^{4} - y^{4}) (x^{4} + y^{4}) = (x^{4})^{2} - (y^{4})^{2} = x^{8} - y^{8} (i i) (2 x - 1) (2 x + 1) (4 x^{2} + 1) (16 x^{4} + 1) = [(2 x)^{2} - (1)^{2}] (4 x^{2} + 1) (16 x^{4} + 1) = (4 x^{2} - 1) (4 x^{2} + 1) (16 x^{4} + 1) = [(4 x^{2})^{2} - (1)^{2}] (16 x^{4} + 1) = (16 x^{4} - 1) (16 x^{4} + 1) = (16 x^{4})^{2} - (1)^{2} = 256 x^{8} - 1 (i i i) (7 m - 8 n)^{2} + (7 m + 8 n)^{2} = (7 m)^{2} + (8 n)^{2} - 2 \times 7 m \times 8 n + (7 m)^{2} + (8 n)^{2} + 2 \times 7 m \times 8 n = 49 m^{2} + 64 n^{2} - 112 m n + 49 m^{2} + 64 n^{2} + 112 m n = 98 m^{2} + 128 n^{2} (i v) (2.5 p - 1.5 q)^{2} - (1.5 p - 2.5 q)^{2} = (2.5 p)^{2} + (1.5 q)^{2} - 2 \times 2.5 p \times 1.5 q - [(1.5 p)^{2} + (2.5 q)^{2} - 2 \times 1.5 p \times 2.5 q] = (6.25 p^{2} + 2.25 q^{2} - 7.5 p q) - (2.25 p^{2} + 6.25 q^{2} - 7.5 p q) = 6.25 p^{2} + 2.25 q^{2} - 7.5 p q - 2.25 p^{2} - 6.25 q^{2} + 7.5 p q = 6.25 p^{2} - 2.25 p^{2} + 2.25 q^{2} - 6.25 q^{2} = 4.00 p^{2} - 4.00 q^{2} = 4 p^{2} - 4 q^{2} = 4 (p^{2} - q^{2}) (v) (m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2} = (m^{2})^{2} + (n^{2} m)^{2} - 2 \times m^{2} \times n^{2} m + 2 m^{3} n^{2} = m^{4} + n^{4} m^{2} - 2 m^{3} n^{2} + 2 m^{3} n^{2} = m^{4} + n^{4} m^{2} = m^{4} + m^{2} n^{4}$

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Q. Simplify and find the value of the algebric expression if m=5 and n=10.

(i) {(m^{2} - n^{2} m)}^{2} + 2 m^{3} n^{2}

(i i) {(7 m - 8 n)}^{2} + {(7 m + 8 n)}^{2}

Simplify and find the value of the algebric expression if m=5 and n=10.

$(i) {(m^{2} - n^{2} m)}^{2} + 2 m^{3} n^{2}$

$(i i) {(7 m - 8 n)}^{2} + {(7 m + 8 n)}^{2}$

$(i i i) {(m^{2} - n^{2})}^{2}$ [3 MARKS]

Q. Simplify:

(7 m - 8 n)^{2} + (7 m + 8 n)^{2}

Q. Simplify:

(2.5 p - 1.5 q)^{2} - (1.5 p - 2.5 q)^{2}

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Simplify: (i) (x−y)(x+y)(x2+y2)(x4+y4) (ii) (2x−1)(2x+1)(4x2+1)(16x4+1) (iii) (7m−8n)2+(7m+8n)2 (iv) (2.5p−1.5q)2−(1.5p−2.5q)2 (v) (m2−n2m)2+2m3n2

Simplify:

$(i) (x - y) (x + y) (x^{2} + y^{2}) (x^{4} + y^{4})$ $(i i) (2 x - 1) (2 x + 1) (4 x^{2} + 1) (16 x^{4} + 1)$

$(i i i) (7 m - 8 n)^{2} + (7 m + 8 n)^{2}$ $(i v) (2.5 p - 1.5 q)^{2} - (1.5 p - 2.5 q)^{2}$

$(v) (m^{2} - n^{2} m)^{2} + 2 m^{3} n^{2}$