Expand1 a-2a-12 m-4m-63 p-8p-34 13-x13-x5 3 x-4 y3 x-5 y6 9 x-5 t9 x-3 t7 m -23 m -738 x-1 x x-1 x9 1 y -41 y -9

It is known that,(x+a)(x+b)=x^2+(a+b)x+ab(1) nbsp; (a+2)(a 1)=a^2+(2+ 1)a+(2× 1) =a^2+1(a) 2 =x^2+a 2(2) (m 4)(m+6)=m^2+( 4+6)m+( 4×6) =m^2+ nbsp;2m 24(3) ...

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Byju's Answer

Standard XII

Mathematics

Property 4

Expand1 a+2a-...

Question

Expand:
(1) $(a + 2) (a - 1)$
(2) $(m - 4) (m + 6)$
(3) $(p + 8) (p - 3)$
(4) $(13 + x) (13 - x)$
(5) $(3 x + 4 y) (3 x + 5 y)$
(6) $(9 x - 5 t) (9 x + 3 t)$
(7) $(m + \frac{2}{3}) (m - \frac{7}{3})$
(8) $(x + \frac{1}{x}) (x - \frac{1}{x})$
(9) $(\frac{1}{y} + 4) (\frac{1}{y} - 9)$

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Solution

It is known that,
$(x + a) (x + b) = x^{2} + (a + b) x + a b$
(1)
$(a + 2) (a - 1) = a^{2} + (2 + - 1) a + (2 \times - 1) = a^{2} + 1 (a) - 2 = x^{2} + a - 2$
(2)
$(m - 4) (m + 6) = m^{2} + (- 4 + 6) m + (- 4 \times 6) = m^{2} + 2 m - 24$

(3)
$(p + 8) (p - 3) = p^{2} + (8 + - 3) p + (8 \times - 3) = p^{2} + 5 p - 24$

(4)
It is known that, $(a + b) (a - b) = a^{2} - b^{2}$
$(13 + x) (13 - x) = (13)^{2} - x^{2} = 169 - x^{2}$

(5) $(3 x + 4 y) (3 x + 5 y) = (3 x)^{2} + (4 y + 5 y) 3 x + (4 y \times 5 y) = 9 x^{2} + (9 y \times 3 x) + 20 y^{2} = 9 x^{2} + 27 x y + 20 y^{2}$

(6) $(9 x - 5 t) (9 x + 3 t) = (9 x)^{2} + (- 5 t + 3 t) 9 x + - (5 t \times 3 t) = 81 x^{2} + (- 2 t) 9 x - 15 t^{2} = 81 x^{2} - 18 x t - 15 t^{2}$
(7) $(m + \frac{2}{3}) (m - \frac{7}{3}) = m^{2} + (\frac{2}{3} + - \frac{7}{3}) m + (\frac{2}{3} \times \frac{- 7}{3}) = m^{2} - \frac{(5 m)}{3} - \frac{14}{9}$

(8)
It is known that
$(a + b) (a - b) = a^{2} - b^{2}$
$(x + \frac{1}{x}) (x - \frac{1}{x}) = x^{2} - \frac{1}{x^{2}}$

(9)
$(\frac{1}{y} + 4) (\frac{1}{y} - 9) = \frac{1}{y^{2}} + (4 + - 9) \frac{1}{y} + (4 \times - 9) = \frac{1}{y^{2}} + \frac{- 5}{y} - 36$

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Similar questions

Q. If

\int x^{13 / 2} . {(1 + x^{5 / 2})}^{1 / 2} d x = p {(1 + x^{5 / 2})}^{7 / 2} + Q {(1 + x^{5 / 2})}^{5 / 2} + R {(1 + x^{5 / 2})}^{3 / 2} + C

, then P, Q and R are

(a) (m × 4m) − (3m⁴ ÷ m²)

(b) (x⁵ ÷ x³) + 3x²

p (x) = 63 - 9 x

is a _______ polynomial.

Q. If

x^{15} - x^{13} + x^{11} - x^{9} + x^{7} - x^{5} + x^{3} - x = 7

then

Q. Simplify:

(1)

18^{\frac{1}{4}} \times 18^{\frac{1}{5}}

(2)

7^{\frac{1}{3}} \div 7^{\frac{1}{5}}

(3)

{(4^{\frac{1}{2}})}^{\frac{1}{9}}

(4)

{(9 \times 5)}^{\frac{1}{6}}

(5)

x^{\frac{1}{7}} \div x^{\frac{1}{10}}

(6)

{(x y)}^{\frac{1}{2}}

(7)

{(y^{\frac{1}{3}})}^{\frac{1}{2}}

(8)

{(m^{\frac{1}{3}})}^{\frac{1}{7}}

(9)

p^{\frac{1}{2}} \times p^{\frac{1}{2}}

(10)

m^{\frac{1}{3}} \times m^{\frac{1}{3}}

(11)

{(7 \times 9)}^{\frac{1}{5}}

(12)

{(m n)}^{\frac{1}{p}}

(13)

x^{\frac{1}{8}} \div x^{\frac{1}{11}}

(14)

x^{\frac{1}{2}} \div x^{\frac{1}{2}}

(15)

{(13 \div 15)}^{\frac{1}{7}}

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Expand: (1)(a+2)(a−1)(2) (m−4)(m+6)(3) (p+8)(p−3)(4) (13+x)(13−x)(5) (3x+4y)(3x+5y)(6) (9x−5t)(9x+3t)(7) (m+23)(m−73)(8) (x+1x)(x−1x)(9) (1y+4)(1y−9)

Expand:
(1) $(a + 2) (a - 1)$
(2) $(m - 4) (m + 6)$
(3) $(p + 8) (p - 3)$
(4) $(13 + x) (13 - x)$
(5) $(3 x + 4 y) (3 x + 5 y)$
(6) $(9 x - 5 t) (9 x + 3 t)$
(7) $(m + \frac{2}{3}) (m - \frac{7}{3})$
(8) $(x + \frac{1}{x}) (x - \frac{1}{x})$
(9) $(\frac{1}{y} + 4) (\frac{1}{y} - 9)$