Question : The value of $(2a+b)^{2}-(2a-b)^{2}$ is:
Option 1: $8ab$
Option 2: $–8ab$
Option 3: $8a^{2}+2b^{2}$
Option 4: $8a^{2}–2b^{2}$
Correct Answer: $8ab$
Solution : Given: $(2a+b)^{2}–(2a–b)^{2}$ We know that: $a^2-b^2=(a+b)(a-b)$ Applying this to expression, we have, = $(2a+b+2a-b)(2a+b-2a+b)$ = $(4a)(2b)$ = $8ab$ Hence, the correct answer is $8ab$.
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Question : If $x=\frac{8ab}{a+b}(a\neq b),$ then the value of $\frac{x+4a}{x–4a}+\frac{x+4b}{x–4b}$ is:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 4
Question : What is the value of $\frac{(a^2+b^2)(a-b)-(a^3-b^3)}{a^2b-ab^2}?$
Option 3: –1
Option 4: 3
Question : What is the value of $\frac{(a^2+b^2)(a-b)-(a-b)^3}{a^2b-ab^2}?$
Option 1: $0$
Option 2: $1$
Option 3: $–1$
Option 4: $2$
Question : If $a,b,c$, and $d$ satisfy the equations: $a+7b+3c+5d=0$, $8a+4b+6c+2d=–4$, $2a+6b+4c+8d=4$, $5a+3b+7c+d=–4$, then $\frac{a+d}{b+c}$?
Option 4: – 4
Question : The value of –7 ÷ [5 + 1 ÷ 2 – {4 + (4 of 2 ÷ 4) + (4 ÷ 4 of 2)}] is:
Option 1: $-\frac{7}{2}$
Option 2: $–7$
Option 3: $\frac{7}{2}$
Option 4: $7$
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