Question

Mathematics class 7 (please answer correctly) !!!
1. simplify by combining like terms
(a) 15b-30+7b-20
(b) 5x²y-5x²+2yx²-3y²+8xy²
2. Find the numbers from the expanded form
(a) 4×10³+3×10²+5×10
(b) 3×10⁵+5×10³+2×10²+4×10+7×10°
3. Simplify
(a) 3²×p²×2³×p
(b) (2×3⁴×2⁵) ÷ (3²×2⁴)
please try to answer all

Answer 1

αnswers :-

1. Simplify by combining the like terms :  

$\sf \bullet \;\; a) \;\; 15b-30+7b-20$

$\sf \implies 15b+7b-30-20$

$\sf \implies 22b-50$  

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$\sf \bullet \;\; b) \;\;5x^{2}y-5x^{2}+2yx^{2}-3y^{2}+8xy^{2}$

$\sf \implies 5x^{2} + 2x^{2}y-5x^{2}+8xy^{2}$

__________

~Here,

• $\sf 2yx^{2} \;\;is\;written\;as\;2x^{2}y$

Both are same

__________

$\sf \implies 7x^{2}-5x^{2}+8xy^{2}$

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2 ) Find the numbers from the expanded form

(a) 4×10³+3×10²+5×10

$\sf \implies 4 \times 1000 + 3 \times 100 + 5 \times 10$  

$\sf \implies 4000 + 300 + 50$

$\sf \implies 4350$

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(b) 3×10⁵+5×10³+2×10²+4×10+7×10°

$\sf \implies 3 \times 100000 + 5 \times 1000 + 2 \times 100 + 4 \times 10 + 7 \times 1$

__________

~Here,  

• $\sf 10^{0} \;\;is\;written\;as\;1$

 

Because any number raised to the power 0 is always 1

__________

$\sf \implies 300000 + 5000 + 200 + 40 + 7$

$\sf \implies 305247$

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2. Simplify

(a) 3²×p²×2³×p

$\sf \implies 3^{2} \times p^{2} \times 2^{3} \times p^{1}$

$\sf \implies 3^{2} \times p^{2+1} \times 2^{3}$

$\sf \maltese \;\; \bigg\{ Rule\;used\;= m^{n} \times m^{s} = m^{(n+s)} \bigg\}$  

$\sf \implies 3^{2} \times p^{3} \times 2^{3}$

$\sf \maltese \;\; \bigg\{ Rule\;used = m^{n} \times s^{n} = (ms)^{n} \bigg\}$

$\sf \implies 3^{2}p^{3} \times 2^{3}$

$\sf \implies 9p^{3} \times 8$

$\sf \implies 72p^{3}$

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(b) (2×3⁴×2⁵) ÷ (3²×2⁴)

$\sf \implies ( 2^{1} \times 3^{4} \times 2^{5} ) \div ( 3^{2} \times 2^{4} )$  

$\sf \maltese \;\; \bigg\{ Rule\;used\;= m^{n} \times m^{s} = m^{n+s} \bigg\}$

$\sf \implies ( 2^{1+5} \times 3^{4} ) \div ( 3^{2} \times 2^{4})$

$\sf \implies ( 2^{6} \times 3^{4} ) \div ( 3^{2} \times 2^{4} )$

$\sf \maltese \;\; \bigg\{ Rule\;used\;= m^{n} \div m^{s} = m^{n-s} \bigg\}$

$\sf \implies ( 2^{6-4} \times 3^{4-2} )$  

$\sf \implies ( 2^{2} \times 3^{2} )$  

$\sf \maltese \;\; \bigg\{ Rule\;used = m^{n} \times s^{n} = (ms)^{n} \bigg\}$

 

$\sf \implies (2 \times 3)^{2}$

$\sf \implies 6^{2}$

$\sf \implies 36$

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