Question

Say whether the following statements are True or False: (i) (7x+3)(7x-4) = 49x²-7x-12 (ii) (a-1)² = a² - 1 (iii) (x²+y²)(y²+x²) = (x²+y²)² (iv) 2p is the factor of 8pq. (Explain the sum and give correct answer)​

Answer 1

$i) (7x+3)(7x-4) = 49x^{2} - 7x - 12$

$LHS = (7x+3)(7x-4) \\= (7x)^{2} + (3-4)7x+3\times(-4)$

$\underline { \blue { By \: algebraic \: identity :}}$

$\boxed { \pink { (x+m)(x+n) = x^{2} +(m+n)x + mn }}$

$= 49x^{2}+(-1)7x-12\\= 49x^{2}-7x-12 \\= RHS$

Therefore.,

$(7x+3)(7x-4) = 49x^{2} - 7x - 12\:\pink{(True)}$

$ii) (a-1)^{2} = a^{2}-1$

$LHS = (a-1)^{2} \\= a^{2} - 2\times a \times 1 + 1^{2} \\= a^{2} - 2a + 1 \\ \neq RHS$

Therefore.,

$(a-1)^{2} = a^{2}-1 \: \pink { ( False )}$

$iii) (x^{2}+y^{2})(y^{2}+x^{2}) = (x^{2}+y^{2})^{2}$

$LHS = (x^{2}+y^{2})(y^{2}+x^{2})\\= (x^{2}+y^{2})(x^{2}+y^{2})\\= (x^{2}+y^{2})^{2}\\= RHS$

Therefore.,

$(x^{2}+y^{2})(y^{2}+x^{2}) = (x^{2}+y^{2})^{2}\\\pink {(True)}$

$iv) 2p\:is \:the \: factor \:of \:8pq$

$8pq = 2p \times (4q) \\= 2p \:is \:a \:factor \:of \:8pq$

Therefore.,

$2p\:is \:the \: factor \:of \:8pq \:\pink {(True )}$

•••♪

Answer 2

Step-by-step explanation:

2p is the factor of 8pq. say true or false